ORIGINAL_ARTICLE
Non-Equivalent Norms on $C^b(K)$
Let $A$ be a non-zero normed vector space and let $K=\overline{B_1^{(0)}}$ be the closed unit ball of $A$. Also, let $\varphi$ be a non-zero element of $ A^*$ such that $\Vert \varphi \Vert\leq 1$. We first define a new norm $\Vert \cdot \Vert_\varphi$ on $C^b(K)$, that is a non-complete, non-algebraic norm and also non-equivalent to the norm $\Vert \cdot \Vert_\infty$. We next show that for $0\neq\psi\in A^*$ with $\Vert \psi \Vert\leq 1$, the two norms $\Vert \cdot \Vert_\varphi$ and $\Vert \cdot \Vert_\psi$ are equivalent if and only if $\varphi$ and $\psi$ are linearly dependent. Also by applying the norm $\Vert \cdot \Vert_\varphi $ and a new product `` $\cdot$ '' on $C^b(K)$, we present the normed algebra $ \left( C^{b\varphi}(K), \Vert \cdot \Vert_\varphi \right)$. Finally we investigate some relations between strongly zero-product preserving maps on $C^b(K)$ and $C^{b\varphi}(K)$.
https://scma.maragheh.ac.ir/article_44696_f8ab5402f7af7d2d59f42fcd0b311ec3.pdf
2020-11-01
1
11
10.22130/scma.2020.121559.748
Normed vector space
Equivalent norm
Zero-product preserving map
Strongly zero-product preserving map
Ali Reza
Khoddami
khoddami.alireza@shahroodut.ac.ir
1
Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran.
LEAD_AUTHOR
[1] H.G. Dales, Banach Algebras and Automatic Continuity, London Math. Soc. Monogr. Ser., 24 The Clarendon Press, Oxford University Press, New York, (2000).
1
[2] R.A. Kamyabi-Gol and M. Janfada, Banach algebras related to the elements of the unit ball of a Banach algebra, Taiwan. J. Math., 12 (2008), pp. 1769-1779.
2
[3] A.R. Khoddami, On maps preserving strongly zero-products, Chamchuri J. Math., 7 (2015), pp. 16-23.
3
[4] A.R. Khoddami, Strongly zero-product preserving maps on normed algebras induced by a bounded linear functional, Khayyam J. Math., 1 (2015), pp. 107-114.
4
[5] A.R. Khoddami, On strongly Jordan zero-product preserving maps, Sahand Commun. Math. Anal., 3 (2016), pp. 53-61.
5
[6] A.R. Khoddami, The second dual of strongly zero-product preserving maps, Bull. Iran. Math. Soc., 43 (2017), pp. 1781-1790.
6
[7] A.R. Khoddami, Bounded and continuous functions on the closed unit ball of a normed vector space equipped with a new product, U.P.B. Sci. Bull., Series A, 81 (2019), pp. 81-86.
7
[8] A.R. Khoddami, Biflatness, biprojectivity, $varphi-$amenability and $varphi-$contractibility of a certain class of Banach algebras, U.P.B. Sci. Bull., Series A, 80 (2018), pp. 169-178.
8
[9] T.W. Palmer, Banach Algebras and The General Theory of $*-$Algebras, Cambridge University Press, (1994).
9
ORIGINAL_ARTICLE
On Certain Generalized Bazilevic type Functions Associated with Conic Regions
Let $f$ and $g$ be analytic in the open unit disc and, for $\alpha ,$ $\beta \geq 0$, let\begin{align*}J\left( \alpha ,\beta ,f,g\right) & =\frac{zf^{\prime }(z)}{f^{1-\alpha}(z)g^{\alpha }(z)}+\beta \left( 1+\frac{zf^{\prime \prime }(z)}{f^{\prime}(z)}\right) -\beta \left( 1-\alpha \right) \frac{zf^{\prime }(z)}{f(z)} \\& \quad -\alpha \beta \frac{zg^{\prime }(z)}{g(z)}\text{.}\end{align*}The main aim of this paper is to study the class of analytic functions which map $J\left( \alpha ,\beta ,f,g\right) $ onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.
https://scma.maragheh.ac.ir/article_44698_63eca2db22e066ad9caddd3470fea010.pdf
2020-11-01
13
23
10.22130/scma.2020.118014.720
Conic regions
Bazilevic function
Bounded boundary rotation
Hankel determinant
Univalent functions
Khalida Inayat
Noor
khalidan@gmail.com
1
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan.
AUTHOR
Shujaat Ali
Shah
shahglike@yahoo.com
2
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan.
LEAD_AUTHOR
[1] D.A. Brannan, On functions of bounded boundary rotation, Proc. Edinburg Math. Soc., 16 (1969), pp. 339-347.
1
[2] G.M. Golusin, On distortion theorem and coefficients of univalent functions, Math. Sb., 19 (1946), pp. 183-203.
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[3] A.W. Goodman, Univalent Functions, Vols. I & II, Polygonal Publishing House, Washington, New Jersey, (1983).
3
[4] W. K. Hayman, On functions with positive real part, J. London Math. Soc., 36 (1961), pp. 34-48.
4
[5] W.K. Hayman, On the second Hankel determinant of mean univalent functions, Proc. London Math. Soc., 18 (1968), pp. 77-84.
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[6] S. Kanas and A. Wisniowska, Conic domain and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), pp. 647-657.
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[7] S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Math., 105 (1999), pp. 327-336.
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[8] W. Kaplan, Close-to-convex Schlicht functions, Mich. Math. J., 1 (1952), pp. 169-185.
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[9] S.S. Miller and P.T. Mocanu, Differential subordinations theory and applications, Marcel Dekker, Inc., New York, Basel, (2000).
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[10] J.W. Noonan and D.K. Thomas, On the Hankel determinant of areally mean p-valent functions, Proc. London Math. Soc., 25 (1972), pp. 503-524.
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[11] K.I. Noor, Hankel determinant problem for functions of bounded boundary rotations, Rev. Roum. Math. Pures Appl., 28 (1983), pp. 731-739.
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[12] K.I. Noor, On a generalization of close-to-convexity, Int. J. Math. Math. Sci., 6 (1983), pp. 327-334.
12
[13] K.I. Noor, On the Hankel determinant of close-to-convex univalent functions, Inter. J. Math. Sci., 3 (1980), pp. 447-481.
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[14] K.I. Noor, K. Ahmad, On higher order Bazilevic functions, Int. J. Mod. Phys. B, 27(2013), 14 pages.
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[15] K.I. Noor, On the Hankel determinant problem for strongly close-to-convex functions, J. Natu. Geom., 11 (1997), pp. 29-34.
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[16] K.I. Noor and Al-Naggar, Hankel determinant problem, J. Natu. Geom., 14 (1998), pp. 133-140.
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[17] K.I. Noor and M.A. Noor, Higher order close-to-convex functions related with conic domains, Appl. Math. Inf. Sci., 8 (2014), pp. 2455-2463.
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[18] K.S. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math., 31 (1975), pp. 311-323.
18
[19] B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math., 10 (1971), pp. 7-16.
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[20] Ch. Pommerenke, On starlike and close-to-convex functions, Proc. London Math. Soc., 13 (1963), pp. 290-304.
20
[21] D.K. Thomas, On Bazilevic functions, Trans. Amer. Math. Soc., 132 (1968), pp. 353-361.
21
ORIGINAL_ARTICLE
On Measure Chaotic Dynamical Systems
In this paper, we introduce chaotic measure for discrete and continuous dynamical systems and study some properties of measure chaotic systems. Also relationship between chaotic measure, ergodic and expansive measures is investigated. Finally, we prove a new version of variational principle for chaotic measure.
https://scma.maragheh.ac.ir/article_44724_76235e332253a166f905e8c43eaa33b2.pdf
2020-11-01
25
37
10.22130/scma.2020.119707.736
chaos
Chaotic measure
Sensitivity
Faride
Ghorbani Moghaddam
faride.ghorbanimoghaddam@mail.um.ac.ir
1
Department of pure mathematics, Ferdowsi university of Mashhad, Mashhad, Iran.
AUTHOR
Alireza
Zamani Bahabadi
zamany@um.ac.ir
2
Department of pure mathematics, Ferdowsi university of Mashhad, Mashhad, Iran.
LEAD_AUTHOR
Bahman
Honary
honary@um.ac.ir
3
Department of pure mathematics, Ferdowsi university of Mashhad, Mashhad, Iran.
AUTHOR
[1] A. Arbieto and C.A. Morales, Expansivity of ergodic measures with positive entropy, ArXiv: 1110.5598 [math.DS], 2011.
1
[2] J. Banks, J. Brooks, G. Cairns and P. Stacey, On devaney’s definition of chaos, Amer. Math. Monthly, 99 (1992), pp. 332-334.
2
[3] R. Bowen and P. Walters, Expansive one-parameter flows, J. Differential Equations, 12 (1972), pp. 180-193.
3
[4] B. Cadre and P. Jacob, On pairwise sensitivity, J. Math. Anal. Appl., 309 (2005), pp. 375-382.
4
[5] D. Carrasco-Olivera and C. A. Morales, Expansive measures for flows, J. Differential Equations, 256 (2014), pp. 2246–2260.
5
[6] L. He, X. Yan and L. Wang, Weak-mixing implies sensitive dependence, J. Math. Anal. Appl., 299 (2004), pp. 300-304.
6
[7] J. James, T. Koberda, k. Lindsey, P. Speh and C. E. Silva, Measurable Sensitivity, Proc. Amer. Math. Soc., 136 (2008), pp. 3549-3559.
7
[8] L. Lam, Introduction to Nonlinear Physics, Springer Verlag, New York, 1997.
8
[9] C.A. Morales, Measure-expansive Systems, Preprint, IMPA, D083, (2011).
9
[10] W. Sun and E. Vargas, Entropy of flows, Revisited. Bol. Soc. Brasil. Math. (N.S.), 30 (1999), pp. 315-333.
10
[11] W. Sun, T. Young and Y. Zhou, Topological entropies of equivalent smooth flows, Trans. Amer. Math. Soc., 361 (2009), pp. 3071-3082.
11
[12] R.Thakur and R. Das, Devaney chaos and stronger forms of sensitivity on the product of semiflows, Semigroup Forum, 98 (2019), pp. 631–644.
12
[13] P. Varandas, Entropy and Poincare recurrence from a geometrical viewpoint, Nonlinearity, 22 (2009), pp. 2365-2375.
13
[14] P. Walters, An introduction to ergodic theory, Springer Verlag, New York, 1982.
14
[15] A. Wilkinson, Smooth ergodic theory, In Mathematics of complexity and dynamical systems. Springer, New York, 2012.
15
[16] L.S. Young, Entropy in dynamical systems, Princeton University Press, (2003), pp. 313–328.
16
ORIGINAL_ARTICLE
First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras
Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $\ell^1(S)$ with coefficients in $\ell^\infty(S)$ (and also $\ell^1(S)^{(2n-1)}$ for $n\in \mathbb{N}$) are equal.
https://scma.maragheh.ac.ir/article_40586_5458e5df20198923439361c04560b111.pdf
2020-11-01
39
47
10.22130/scma.2020.119494.733
Clifford semigroup
Weak amenability
Weak module amenability
Cohomology group
Module cohomology group
Ebrahim
Nasrabadi
nasrabadi@birjand.ac.ir
1
Faculty of Mathematics Science and Statistics, University of Birjand, Birjand, 9717851367, Iran.
LEAD_AUTHOR
[1] M. Amini, Module amenability for semigroup algebras, Semigroup Forum., 69 (2004), pp. 243-254.
1
[2] M. Amini and D. E. Bagha, Weak module amenability for semigroup algebras, Semigroup Forum., 71 (2005), pp. 18-26.
2
[3] S. Bowling and J. Duncan, First order cohomology of Banach semigroup algebras, Semigroup Forum., 56 (1998), pp. 130-145.
3
[4] H.G. Dales and J. Duncan, Second order cohomology in groups of some semigroup algebras, (Banach Algebra 97 (Blaubeuren) Walter de Gruyter, Berlin), (1998), pp. 101-117.
4
[5] M. Despi´c and F. Ghahramani, Weak amenability of group algebras of locally compact groups, Canad. Math. Bull, 37 (1994), pp. 165-167.
5
[6] F. Gourdeau, A.R. Pourabbas and M.C. White, Simplicial cohomology of some semigroup algebras, Can. Math. Bull, 50 (2007), pp. 56-70.
6
[7] A.Y. Helemskii, The homology of Banach and topological algebras, Moscow Univ. Press. Moscow (1986); English transl, Kluwer Academic Publishers, Dordrecht, (1989)
7
[8] B.E. Johnson, Cohomology in Banach algebras, Mem. Am. Math. Soc, 127, 96 (1972)
8
[9] B.E. Johnson, Weak amenability of group algebras, Bull. London Math. Soc, 23 , (1991), pp. 281-284.
9
[10] E. Nasrabadi, The equality of Hochschild cohomology group and module cohomology group for semigroup algebras, Bol. Soc. Paran. Mat., (2020), In press, DOI:10.5269/bspm.44931.
10
[11] E. Nasrabadi and A. Pourabbas, Module cohomology group of inverse semigroup algebras, Bull. Iranian Math. Soc., 37 , (2011), pp. 157-169.
11
[12] E. Nasrabadi and A. Pourabbas, Second module cohomology group of inverse semigroup algebras, Semigroup Fourm., 81 , (2010), pp. 269-278.
12
[13] A. Shirinkalam, A.R. Pourabbas and M. Amini, Module and Hochschild cohomology of certain semigroup algebras, Funct. Anal. Appl., 49 , (2015), pp. 315-318.
13
ORIGINAL_ARTICLE
Using Copulas to Model Dependence Between Crude Oil Prices of West Texas Intermediate and Brent-Europe
In this study the main endeavor is to model dependence structure between crude oil prices of West Texas Intermediate (WTI) and Brent - Europe. The main activity is on concentrating copula technique which is powerful technique in modeling dependence structures. Beside several well known Archimedean copulas, three new Archimedean families are used which have recently presented to the literature. Moreover, convex combination of these copulas also are investigated on modeling of the mentioned dependence structure. Modeling process is relied on 318 data which are average of the monthly prices from Jun-1992 to Oct-2018.
https://scma.maragheh.ac.ir/article_40585_6cd919a3846d83fe93955345a97b2f3e.pdf
2020-11-01
49
59
10.22130/scma.2020.117584.713
Akaike information criterion (AIC)
Copulas
Goodness of fit test (GOF)
Linear convex combination
Parameter estimation
Vadoud
Najjari
fnajjary@yahoo.com
1
Young Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.
LEAD_AUTHOR
[1] M. Al-Harthy, S. Begg and B. Bratvold Reidar, Copulas: A new technique to model dependence in petroleum decision making, Journal of Petroleum Science and Engineering, 57 (2007), pp. 195-208.
1
[2] T. Bacigal and M. Komornikova, Fitting Archimedean copulas to bivariate geodetic data, COMPSTAT, (2006), pp. 649-656.
2
[3] H. Bal and V. Najjari, Archimedean copulas family via hyperbolic generator, GU J. Sci., 26 (2013), pp. 195-200.
3
[4] P. Bertail, P. Doukhan and P. Soulier, Dependence in Probability and Statistics, Springer Science, LLC, (2006).
4
[5] R.T. Clemen and T. Reilly, Correlations and Copulas for Decision and Risk Analysis, Management Science, 45 (1999), pp. 208-224.
5
[6] S. Celebioglu, Archimedean copulas And An Application, Selcuk University Journal of Science, 22 (2003), pp. 43-52.
6
[7] E.W. Frees and E.A. Valdez, Understanding Relationships Using Copulas, N. Am. Actuar. J., 2 (1998), pp. 1-25.
7
[8] A. Friend and E. Rogge, Correlation at First Sight, Economic Notes: Review of Banking, Finance and Monetary Economics, (2004).
8
[9] C. Genest and J. MacKay, Copules archimedienneset familles de loisbi dimensionnelles dont les margessontdonnees, Canad. J. Stat., 14 (1986a), pp. 145-159.
9
[10] C. Genest and J. MacKay, The joy of copula, Bivariate distributions with uniformmarginals, Amer. Stat., 40 (1986b), pp. 280-285.
10
[11] C. Genest, K. Ghoudi and L.P. Rivest, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82 (1995), pp. 543-552.
11
[12] C. Genest and L.P. Rivest, Statistical Inference Procedures for Bivariate Archimedean copulas, J. Am. Stat. Assoc., 88:423 (1993), pp. 1034-1043.
12
[13] C. Genest, B. Remillard and D. Beaudion, Goodness-of-fit tests for copulas: A review and a power study, Insurance: Mathematics and Economics, 44 (2009), pp. 199-213.
13
[14] L. Hua and H. Joe, Tail order and intermediate tail dependence of multivariate copulas, J. Multivariate Anal., 102 (2011), pp. 1454-1471.
14
[15] Z. Hui-Ming, L. Rong and L. Sufang, Modelling dynamic dependence between crude oil prices and Asia-Pacific stock market returns, International Review of Economics and Finance, 29 (2014), pp. 208-223.
15
[16] H. Joe, Asymptotic efficiency of the two-stage estimation method for copula-based models, J. Multivariate Anal., 94 (2005), pp. 401-419.
16
[17] H. Joe, Multivariate Models and Dependence Concepts, Chapman-Hall, London, (1997).
17
[18] I. Kojadinovic and J. Yan, Tests of serial independence for continuous multivariate time series based on a Mobius decomposition of the independence empirical copula process, Ann. Inst. Stat. Math., 63 (2011), pp. 347-373.
18
[19] D.D. Mari and S. Kotz, Correlation and Dependence, Imperial College Press, London, U.K, (2001).
19
[20] V. Najjari, T. Bacigal and H. Bal, An Archimedean copula family with hyperbolic cotangent generator, Int. J. Unc. Fuzz. Knowl. Based Syst., 22 (2014).
20
[21] V. Najjari, H. Bal and S. celebioglu, Modeling of Dependence Structures in Meteorological Data Via Archimedean Copulas, U.P.B. Sci. Bull., Series D, 75:3: (2013), pp. 131-138.
21
[22] V. Najjari, H. Bal, F. Ozturk and I. Alp, Stochastic Frontier Models By Copulas and An Application, U.P.B. Sci. Bull., Series A, 78 (2016).
22
[23] R.B. Nelsen, An introduction to copulas, Springer, New York, (2006), (Second edition).
23
[24] A. Pirmoradian and A. Hamzah, Simulation of Tail Dependence in cot-copula, Proceedings of the 58th WSC of the ISI, (2011).
24
[25] B. Schweizer, Thirty years of copulas. In: DallAglio G, Kotz S, Salinetti G (eds) Advances in Probability Distributions with Given Marginals, Kluwer, Dordrecht, (1991), pp. 13-50.
25
[26] P.X-K. Song, Correlated Data Analysis: Modeling, Analytics, and Applications, Springer Science, LLC, (2007).
26
[27] H. Tsukahara, Semiparametric estimation in copula models, Canad. J. Stat., 33 (2005), pp. 357-375.
27
ORIGINAL_ARTICLE
Integral Operators on the Besov Spaces and Subclasses of Univalent Functions
In this note, we study the integral operators $I_{g}^{\gamma, \alpha}$ and $J_{g}^{\gamma, \alpha}$ of an analytic function $g$ on convex and starlike functions of a complex order. Then, we investigate the same operators on $H^{\infty}$ and Besov spaces.
https://scma.maragheh.ac.ir/article_40576_3f061ba4a37d4f807825565e279183a6.pdf
2020-11-01
61
69
10.22130/scma.2019.109347.625
Integral operators
Besov spaces
Convex functions of complex order
Starlike functions of complex order
Schwarzian norm
Zahra
Orouji
z.oroujy@yahoo.com
1
Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.
LEAD_AUTHOR
Ali
Ebadian
ebadian.ali@gmail.com
2
Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.
AUTHOR
[1] J.J. Donaire, D. Girela, and D. Vukotic, On the growth and range of functions in Mobius invariant spaces, J. Anal. Math., 112(1) (2010), pp. 237-260.
1
[2] J.J. Donaire, D. Girela, and D. Vukotic, On univalent functions in some Mobius invariant spaces, J. Reine. Angew. Math., 553 (2002), pp. 43-72.
2
[3] A. Ebadian and J. Sokol, Volterra type operator on the convex functions, Hacet. J. Math. Stat., 47(1) (2018), pp. 57-67.
3
[4] C. Hammond, The norm of a composition operator with linear symbol acting on the Dirichlet space, J. Math. Anal. Appl., 303(2) (2005), pp. 499-508.
4
[5] Y.C. Kim and T. Sugawa, Growth and coefficient estimates for uniformly locally univalent functions on the unit disk, Rocky Mt. J. Math., 32 (2002), pp. 179-200.
5
[6] Y.C. Kim and T. Sugawa, Uniformly locally univalent functions and Hardy spaces, J. Math. Anal. Appl., 353(1) (2009), pp. 61-67.
6
[7] S. Li, Volterra composition operators between weighted bergman spaces and bloch type spaces, J. Korean Math. SOC., 45(1) (2008), pp. 229-248.
7
[8] S. Li and S. Stevic, Integral type operators from mixed-norm spaces to $alpha$-Bloch spaces, Integr. Transf. Spec. F., 18(7) (2007), pp. 485-493.
8
[9] S. Li and S. Stevic, Products of integral-type operators and composition operators between bloch-type spaces, J. Math. Anal. Appl., 349(2) (2009), pp. 596-610.
9
[10] Z. Nehari, A property of convex conformal maps, J. Anal. Math., 30(1) (1976), pp. 390-393.
10
[11] Z. Orouji and R. Aghalary, The norm estimates of pre-schwarzian derivatives of spirallike functions and uniformly convex $ alpha $-spirallike functions, Sahand Commun. Math. Anal., 12(1) (2018), pp. 89-96.
11
[12] M. Taati, S. Moradi, and S. Najafzadeh, Some properties and results for certain subclasses of starlike and convex functions, Sahand Commun. Math. Anal.,7(1) (2017), pp. 1-15.
12
[13] J. Xiao, Holomorphic $Q$ classes, Lecture notes in mathematics, 2001.
13
[14] K. Zhu, Operator theory in function spaces, MR 92c, 47031, 1990.
14
ORIGINAL_ARTICLE
Some Properties of Certain Subclass of Meromorphic Functions Associated with $(p , q)$-derivative
In this paper, by making use of $(p , q) $-derivative operator we introduce a new subclass of meromorphically univalent functions. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Coefficient estimates, extreme points, convex linear combination, Radii of starlikeness and convexity and finally partial sum property are investigated.
https://scma.maragheh.ac.ir/article_46513_ba4bd240373ac817f9a7ad479af9aeef.pdf
2020-11-01
71
84
10.22130/scma.2020.124021.772
Meromorphic function
$(p, q)$-derivative
Coefficient bound
Extreme Point
convex set
Partial sum
Hadamard product
Mohammad Hassan
Golmohammadi
golmohamadi@pnu.ac.ir
1
Department of Mathematics, Payame Noor University (PNU), P.O.Box: 19395-3697, Tehran, Iran.
LEAD_AUTHOR
Shahram
Najafzadeh
najafzadeh4321@yahoo.ie
2
Department of Mathematics, Payame Noor University (PNU), P.O.Box: 19395-3697, Tehran, Iran.
AUTHOR
Mohammad Reza
Foroutan
foroutan_mohammadreza@yahoo.com
3
Department of Mathematics, Payame Noor University (PNU), P.O.Box: 19395-3697, Tehran, Iran.
AUTHOR
[1] M.H. Abu-Risha, M.H. Annaby, M.E.H. Ismail and Z.S. Mansour, Linear $q$-difference equations, Z. Anal. Anwend., 26 (4) (2007), pp. 481-494.
1
[2] D. Albayrak, S.D. Purohit and F. Uçar, On $q$-analogues of sumudu transforms, An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat., 21 (1) (2013), pp. 239-260.
2
[3] R. Chakrabarti, R. Jagannathan, A $(p,q) $-oscillator realization of two-parameter quantum algebras, J. Phys. A., 24 (1991), pp. L711-L718.
3
[4] G. Gasper and M. Rahman, Basic Hypergeometric series, Cambridge University Press, Cambridge, 1990.
4
[5] Z.-G. Wang and M.-L. Li, Some properties of Certain family of Multiplier transforms, Filomat., 31 (1) (2017), pp. 159-173.
5
[6] F.H. Jackson, On $q$-functions and a certain difference operator, Trans. Roy. Soc. Edinb., 46 (1908), pp. 64-72.
6
[7] F.H. Jackson, $q$-definite integrals, Q. J. pure Appl. Math., 41 (1910), pp. 193-203.
7
[8] F.H. Jackson, $q$-Difference equations, Am. J. Math., 32 (1910), pp. 305-314.
8
[9] Z.S.I. Mansour, Linear sequential $q$-difference equations of fractional order, Fract. Calc. Appl. Anal., 12 (2) (2009), pp. 159-178.
9
[10] A.O. Mostafa, M.K. Aouf, H.M. Zayed and T. Bulboaca, Convolution conditions for subelasse of mermorphic functions of complex order associated with basic Bessel functions, J. Egyptian Math. Soc., 25 (2017), pp. 286-290.
10
[11] H.E. Ozkan Ucar, Coefficient inequalties for $q$-starlike functions, Appl. Math. Comput., 276 (2016), pp. 122-126.
11
[12] Y. Polatoglu, Growth and distortion theorems for generalized $q$-starlike functions, Adv. Math. Sci. J., 5 (2016), pp. 7-12.
12
[13] S.D. Purohit and R.K. Raina, Certain subclass of analytic functions associated with fractional $q$-calculus operators, Math. Scand., 109 (2011), pp. 55-70.
13
[14] P.M. Rajkovic, S.D. Marinkovic and M.S. Stankovic, Fractional integrals and derivatives in $q$-calculus, Appl. Anal. Discrete Math., 1 (2007), pp. 311-323.
14
[15] R. Srivastava and H.M. Zayed, Subclasses of analytic functions of complex order definde by $q$-derivative operator, Stud. Univ. Babes-Bolyai Math., 64 (2019), pp. 71-80.
15
[16] M. Tahir, N. Khan, Q.Z. Ahmad, B. Khan and G.M. Khan, Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain, Sahand Commun. Math. Anal., 16 (2019), pp. 69-81.
16
[17] A. Zireh and M.M. Shabani, On the Linear Combinations of Slanted Half-Plane Harmonic Mappings, Sahand Commun. Math. Anal., 14 (2019), pp. 89-96.
17
ORIGINAL_ARTICLE
On the Basicity of Systems of Sines and Cosines with a Linear Phase in Morrey-Type Spaces
In this work systems of sines $\sin \left(n+\beta \right)t,\, \, n=1,2, \ldots,$ and cosines $\cos \left(n-\beta \right)t,\, \, n=0,1,2, \ldots,$ are considered, where $\beta \in R-$is a real parameter. The subspace $M^{p,\alpha } \left(0,\pi \right)$ of the Morrey space $L^{p,\alpha } \left(0,\pi \right)$ in which continuous functions are dense is considered. Criterion for the completeness, minimality and basicity of these systems with respect to the parameter $\beta $ in the subspace $M^{p,\alpha } \left(0,\pi \right)$, $1<p <+\infty, $ are found.
https://scma.maragheh.ac.ir/article_44697_cbd161a29f74c2d58e3208f9743ed543.pdf
2020-11-01
85
93
10.22130/scma.2020.121797.756
Basicity
System of sines
System of cosines
Morrey space
Fidan
Seyidova
seyidova.fidan.95@mail.ru
1
Ganja State University, Ganja, Azerbaijan.
LEAD_AUTHOR
[1] D.R. Adams, Morrey spaces, Switzherland, Springer, 2016.
1
[2] B.T. Bilalov, A system of exponential functions with shift and the Kostyuchenko problem, Sib. Math. J., 50(2) (2009), pp. 223-230.
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[3] B.T. Bilalov, Bases of a system of exponentials in $L_p $, Dokl. Akad. Nauk, 392(5) (2003), pp. 583-585.
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[4] B.T. Bilalov, Basis Properties of Some Systems of Exponents, Cosines and Sines, Sib. Math. J., 45 (2004), pp. 264-273.
4
[5] B.T. Bilalov, On solution of the Kostyuchenko problem, Sib. Math. J., 53(3) (2012), pp. 404-418
5
[6] B.T. Bilalov, The basis property of a perturbed system of exponentials in Morrey-type spaces, Sib. Math. J., 60:2 (2019), pp. 249-271.
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[7] B.T. Bilalov, T.B. Gasymov, A.A. Guliyeva, On solvability of Riemann boundary value problem in Morrey-Hardy classes, Turkish J. Math., 40(50) (2016), 1085-1101.
7
[8] B.T. Bilalov, A.A. Guliyeva, On basicity of the perturbed systems of exponents in Morrey-Lebesgue space, Internat. J. Math., 25:1450054, (2014), pp. 1-10.
8
[9] B.T. Bilalov, Z.G. Guseynov, Basicity criterion for perturbed systems of exponents in Lebesgue spaces with variable summability, Dokl. Akad. Nauk, 436(5) (2011), pp. 586-589.
9
[10] B.T. Bilalov, Z.G. Guseynov, Basicity of a system of exponents with a piece-wise linear phase in variable spaces, Mediterr. J. Math, 9(3) (2012),
10
pp. 487-498.
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[11] B.T. Bilalov, A.A. Huseynli, S.R. El-Shabrawy, Basis Properties of Trigonometric Systems in Weighted Morrey Spaces, Azerb. J. Math., 9(2) (2019), pp. 200-226
12
[12] B.T. Bilalov, F.Sh. Seyidova, Basicity of a system of exponents with a piecewise linear phase in Morrey-type spaces, Turkish J. Math. 43 (2019), pp. 1850-1866
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[13] R.E. Casillo, H. Rafeiro, An introductory course in Lebesgue spaces, Springer, 2016.
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[15] L. Diening, P. Harjuleto, P. Hasto, M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents, Springer, 2011, 509 p.
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[17] V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko, Integral Operators in Non-Standard Function Spaces, Volume 1: Variable Exponent Lebesgue and Amalgam Spaces, Springer, 2016.
18
[18] V. Kokilashvili, A. Meskhi, H. Rafeiro, S. Samko, Integral Operators in Non-Standard Function Spaces, Volume 2: Variable Exponent H"older, Morrey-Campanato and Grand Spaces, Springer, 2016.
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[20] E.I. Moiseev, On basicity of a system of sines, Differ. Equ. 23(1) (1987), pp. 177-179.
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31
ORIGINAL_ARTICLE
Fixed Point Results for Extensions of Orthogonal Contraction on Orthogonal Cone Metric Space
In this paper, some fixed point results of self mapping which is defined on orthogonal cone metric spaces are given by using extensions of orthogonal contractions. And by taking advantage of these results, the necessary conditions for self mappings on orthogonal cone metric space to have P property are investigated. Also an example is given to illustrate the main results.
https://scma.maragheh.ac.ir/article_44725_9a9c557e82dbec241c258f4cb3668669.pdf
2020-11-01
95
107
10.22130/scma.2020.118420.722
Fixed point
Periodic point
Orthogonal set
Orthogonal contraction
Orthogonal cone metric
Nurcan
Bilgili Gungor
bilgilinurcan@gmail.com
1
Department of Mathematics, Faculty of Science and Arts, Amasya University, 05000, Amasya, Turkey.
LEAD_AUTHOR
Duran
Turkoglu
dturkoglu@gazi.edu.tr
2
Department of Mathematics, Faculty of Science, Gazi University, 06500, Ankara, Turkey.
AUTHOR
[1] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Appl. Math. Anal. Appl., 341(1), (2008), pp. 416-420.
1
[2] M. Abbas and B.E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22(4), 2009, pp. 511-515.
2
[3] H. Baghani, M.E. Gordji and M. Ramezani, Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl., 18(3), 2016, pp. 465-477.
3
[4] N. Bilgili Gungor, Orthogonal cone metric spaces and fixed points of orthogonal contractions, Int. J. Nonlinear Anal. Appl., 2019.(to appear)
4
[5] N. Bilgili Gungor and M. Surmelioglu, Some Fixed Point Theorems for Contractive Mappings on Ordered Orthogonal Cone Metric Spaces, Univers. J. Math., 3 (1), 2020, pp. 83-93.
5
[6] M. Gordji and H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algebra , 6(3), 2017, pp. 251-260.
6
[7] M.E. Gordji, M. Ramezani, M. De La Sen and Y.J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2), 2017, pp. 569-578.
7
[8] L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings , J. Math. Anal. Appl., 332(2), 2007, pp. 1468-1476.
8
[9] D. Ilic and V. Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341(2), 2008, pp. 876-882.
9
[10] S. Janković, Z. Kadelburg and S. Radenović, On cone metric spaces: a survey, Nonlinear Anal., Theory Methods Appl., 74(7), 2011, pp. 2591-2601.
10
[11] M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6(2), 2015, pp. 127-132.
11
[12] M. Ramezani and H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl., 8(2), 2017, pp. 23-28.
12
[13] A.C. Ran and M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc., 2004, pp. 1435-1443.
13
[14] S. Rezapour and R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345(2), 2008, pp. 719-724.
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[15] D. Turkoglu and M. Abuloha, Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin., Engl. Ser., 26(3), 2010, pp. 489-496.
15
[16] P. Vetro, Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 56(3),2007, pp. 464-468.
16