ORIGINAL_ARTICLE
The Fekete-Szegö problem for a general class of bi-univalent functions satisfying subordinate conditions
In this work, we obtain the Fekete-Szegö inequalities for the class $P_{\Sigma }\left( \lambda ,\phi \right) $ of bi-univalent functions. The results presented in this paper improve the recent work of Prema and Keerthi [11].
http://scma.maragheh.ac.ir/article_22042_d72f5c70832625d1de77bd8a4dcc14fb.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
1
7
Bi-univalent functions
Convex functions with respect to symmetric points
Subordination
Fekete-Szegö inequality
Şahsene
Altınkaya
sahsene@uludag.edu.tr
true
1
Department of Mathematics, Faculty of Arts and Science, University of Uludag, 16059, Bursa, Turkey.
Department of Mathematics, Faculty of Arts and Science, University of Uludag, 16059, Bursa, Turkey.
Department of Mathematics, Faculty of Arts and Science, University of Uludag, 16059, Bursa, Turkey.
LEAD_AUTHOR
Sibel
Yalҫın
syalcin@uludag.edu.tr
true
2
Department of Mathematics, Faculty of Arts and Science, University of Uludag, 16059, Bursa, Turkey.
Department of Mathematics, Faculty of Arts and Science, University of Uludag, 16059, Bursa, Turkey.
Department of Mathematics, Faculty of Arts and Science, University of Uludag, 16059, Bursa, Turkey.
AUTHOR
[1] Ş. Altinkaya and S. Yalҫin, Initial coefficient bounds for a general class of bi-univalent functions, Inter. J. Anal., Article ID 867871, 2014, 4 pp.
1
[2] D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Stud. Univ. Babeş-Bolyai Math., 31 (2) (1986) 70-77.
2
[3] S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 352 (2014) 479-484.
3
[4] O. Crișan, Coefficient estimates certain subclasses of bi-univalent functions, Gen. Math. Notes, 16 (2013) 93--1002.
4
[5] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, 259, 1983.
5
[6] B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011) 1569-1573.
6
[7] S.G. Hamidi and J.M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser.I, 352 (2014) 17-20.
7
[8] J.M. Jahangiri and S.G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci., ArticleID 190560, (2013) 4 pp.
8
[9] B.S. Keerthi and B. Raja, Coefficient inequality for certain new subclasses of analytic bi-univalent functions, Theoretical Mathematics and Applications, 3 (2013) 1-10.
9
[10] N. Magesh and J. Yamini, Coefficient bounds for a certain subclass of bi-univalent functions, Int. Math. Forum, 8 (2013) 1337-1344.
10
[11] S. Prema and B.S. Keerthi, Coefficient bounds for a certain subclass of analytic functions, J. Math. Anal., 4 (2013) 22-27.
11
[12] C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
12
[13] H.M. Srivastava, A.K. Mishra, and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010) 1188-1192.
13
[14] Q.H. Xu, Y.C. Gui, and H.M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent
14
functions, Appl. Math. Lett., 25 (2012) 990-994.
15
[15] P. Zaprawa, On Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21 (2014) 169-178.
16
ORIGINAL_ARTICLE
Extension of Krull's intersection theorem for fuzzy module
In this article we introduce $\mu$-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between $\mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $\mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $\mu$-adic completion.
http://scma.maragheh.ac.ir/article_21429_30b2b3341076dddace48c4a072784c9e.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
9
20
$mu$-Fuzzy filtered module
Fuzzy inverse system
Fuzzy topological group
Krull's intersection theorem
Ali Reza
Sedighi
sedighi.phd@birjand.ac.ir
true
1
Department of Mathematics, Faculty of mathematics and statistics, University of Birjand, Birjand, Iran.
Department of Mathematics, Faculty of mathematics and statistics, University of Birjand, Birjand, Iran.
Department of Mathematics, Faculty of mathematics and statistics, University of Birjand, Birjand, Iran.
LEAD_AUTHOR
Mohammad Hossein
Hosseini
mhhosseini@birjand.ac.ir
true
2
Department of Mathematics, Faculty mathematics and statistics, University of Birjand, Birjand, Iran.
Department of Mathematics, Faculty mathematics and statistics, University of Birjand, Birjand, Iran.
Department of Mathematics, Faculty mathematics and statistics, University of Birjand, Birjand, Iran.
AUTHOR
[1] I. Chon, Properties of fuzzy topological groups and semigroups, Kangweon-Kyungki Math. Jour, 8, (2000), 103–110.
1
[2] N.S. Gopalakrishnan, Commutative algebra, Oxonian Press Pvt, University of Poona,1984.
2
[3] C. Gunduz(Aras) and S. Bayramov, Inverse and direct system in category of fuzzy modules, Fuzzy Sets, Rough Sets and Multivalued Operations and Applications, 3, (2011), 11-25.
3
[4] K.H. Lee, On fuzzy quotient rings and chain conditions, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math, 7(1), (2000) 33-40.
4
[5] S.R. Lopez-Permouth and D.S. Malik, On Categories of Fuzzy Modules, Information Sciences, 52, (1990), 211-220.
5
[6] D.S. Malik, Fuzzy maximal, radical, and primary ideals of a ring, Information science, 53, (1991), 237-250.
6
[7] D.S. Malik and John.N. Mordeson, Fuzzy direct sums of fuzzy rings, Fuzzy Sets and Systems, 45, (1992), 83-91.
7
[8] J.N. Mordeson and D.S. Malik, Fuzzy Commutative Algebra, World Scientiﬁc, 1998.
8
[9] G.C. Muganda, Free fuzzy modules and their bases, Inform. Sci, 72, (1993), 65-82.
9
[10] V. Murali and B. Makamba, On Krull's intersection theorem of fuzzy ideals, International journal of mathematics and mathematical sciences, 4, (2003), 251-262.
10
[11] C.V. Negoita and D.A. Ralescu, Applications of Fuzzy Sets and System Analysis, Birkhauser, Basel, 1975.
11
[12] A. Rosenfeld, Fuzzy groups, J1. Math. Anal. Appl., 35, (1971), 512-517.
12
[13] L.A. Zadeh, Fuzzy sets, Inform. Control, 81, (1965), 338-353.
13
[14] M.M. Zahedi and A. Ameri, Fuzzy exact sequences in category of fuzzy modules, Jl. Fuzzy Math., 2(2), (1994), 409-424.
14
ORIGINAL_ARTICLE
$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $\mathbb{E}_1^4$
Biharmonic surfaces in Euclidean space $\mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2\rightarrow\mathbb{E}^{3}$ is called biharmonic if $\Delta^2x=0$, where $\Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimentional pseudo-Euclidean space $\mathbb{E}_1^4$ with an additional condition that the principal curvatures are distinct. A hypersurface $x: M^3\rightarrow\mathbb{E}^{4}$ is called $L_k$-biharmonic if $L_k^2x=0$ (for $k=0,1,2$), where $L_k$ is the linearized operator associated to the first variation of $(k+1)$-th mean curvature of $M^3$. Since $L_0=\Delta$, the matter of $L_k$-biharmonicity is a natural generalization of biharmonicity. On any $L_k$-biharmonic spacelike hypersurfaces in $\mathbb{E}_1^4$ with distinct principal curvatures, by, assuming $H_k$ to be constant, we get that $H_{k+1}$ is constant. Furthermore, we show that $L_k$-biharmonic spacelike hypersurfaces in $\mathbb{E}_1^4$ with constant $H_k$ are $k$-maximal.
http://scma.maragheh.ac.ir/article_20589_41cae243cd77692b496d7ab7a304e79b.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
21
30
Spacelike hypersurface
Biharmonic
$L_k$-biharmonic
$k$-maximal
Firooz
Pashaie
f_pashaie@maragheh.ac.ir
true
1
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.
LEAD_AUTHOR
Akram
Mohammadpouri
pouri@tabrizu.ac.ir
true
2
Department of Mathematics, University of Tabriz, Tabriz, Iran.
Department of Mathematics, University of Tabriz, Tabriz, Iran.
Department of Mathematics, University of Tabriz, Tabriz, Iran.
AUTHOR
[1] G.B. Airy, On the strains in the interior of beams, Philos. Trans. R. Soc. London Ser. A, 153 (1863) 49-79.
1
[2] K. Akutagawa and S. Maeta, Biharmonic properly immersed submanifolds in Euclidean spaces, Geom. Ded., 164 (2013) 351-355.
2
[3] L.J. Alias and N. Gurbuz, An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures, Geom. Ded., 121 (2006) 113-127.
3
[4] M. Aminian and S.M.B. Kashani, Lk-biharmonic hypersurfaces in the Euclidean space, Taiwan. J. Math., Online (DOI:10.11650/tjm.18.2014.4830).
4
[5] A. Caminha, On spacelike hypersurfaces of constant sectional curvature lorentz manifolds, J. Geom. phys., 56 (2006) 1144-1174.
5
[6] B.Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, Ser. Pure Math., World Sci. Pub. Co., Singapore (2014).
6
[7] B.Y. Chen, Some open problems and conjetures on submanifolds of finite type, Soochow J. Math., 17 (1991) 169-188.
7
[8] F. Defever, G. Kaimakamis, and V. Papantoniou, Biharmonic hypersurfaces of the 4-dimensional semi-Euclidean space Es4, J. Math. Anal. Appl., 315: 1 (2006) 276286.
8
[9] I. Dimitric, Submanifolds of En with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sin., 20 (1992) 53-65.
9
[10] J. Eells and J.C. Wood, Restrictions on harmonic maps of surfaces, Topology 15 (1976), pp. 263-266.
10
[11] T. Hasanis and T. Vlachos, Hypersurfaces in E4 with harmonic mean curvature vector field, Math. Nachr., 172 (1995) 145-169.
11
[12] S.M.B. Kashani, On some L1-finite type (hyper)surfaces in Rn+1, Bull. Kor. Math. Soc., 46 (1), (2009) 35-43.
12
[13] P. Lucas and H.F. Ramirez-Ospina, Hypersurfaces in the Lorentz-Minkowski space satisfying LkΨ=AΨ+b, Geom. Ded., 153 (2011) 151-175.
13
[14] J.E. Marsden and F. Tipler, Maximal hypersurfaces and foliations of constant mean curvature in general relativity, Phys. Rep. 66 (1980) 109-139.
14
[15] J.C. Maxwell, On reciprocal diagrams in space, and their relation to Airy function of stress, Proc. London. Math. Soc., s1-2(1), (1866) 58-63.
15
[16] A. Mohammadpouri and S.M.B. Kashani, On some Lk-finite type Euclidean hypersurfaces,ISRN Geom. (2012),, Article ID 591296, 23 pages.
16
[17] A. Mohammadpouri, S.M.B. Kashani, and F. Pashaie, On some L1-finite type Euclidean surfaces, Acta Math. Vietnam., 38 (2013) 303316.
17
[18] A. Mohammadpouri and F. Pashaie, Lr-biharmonic hypersurfaces in E4, submitted.
18
[19] B. O'Neill, Semi-Riemannian Geometry with Applicatins to Relativity, Acad. Press Inc., 2nd ed. (1983).
19
[20] R.C. Reilly, Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Diff. Geom., 8(3) (1973) 465-477.
20
[21] B. Segre, Famiglie di ipersuperficie isoparametrische negli spazi euclidei ad un qualunque numero di dimensioni, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur, 27 (1938) 203-207.
21
[22] B.G. Yang and X.M. Liu, r-minimal hypersurfaces in space forms, J. Geom. Phys., 59 (2009) 685-692.
22
ORIGINAL_ARTICLE
A family of positive nonstandard numerical methods with application to Black-Scholes equation
Nonstandard finite difference schemes for the Black-Scholes partial differential equation preserving the positivity property are proposed. Computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the Black-Scholes equation. Unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.
http://scma.maragheh.ac.ir/article_19335_cf08f2d957449d24abc0378c987a3ca6.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
31
40
Black-Scholes equation
Option pricing
Finite difference scheme
Positivity-preserving
Mohammad
Mehdizadeh Khalsaraei
muhammad.mehdizadeh@gmail.com
true
1
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
LEAD_AUTHOR
Nashmil
Osmani
n.osmani2013@gmail.com
true
2
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
AUTHOR
[1] A.J. Arenas, G. Gonzalez-Parra, and B. M. Caraballo, A nonstandard finite difference scheme for a nonlinear Black-Scholes equation, Math. Comput. Model., 57 (2013) 1663-1670.
1
[2] F. Black and M. Scholes, The pricing of options and corporate liabilities, J. politic. Eco., 81 (1973) 637-659.
2
[3] D.J. Duffy, Finite Difference Methods in Financial Engineering, A Partial Differential Equation Approach, John Wiley and Sons, England, 2006.
3
[4] M. Mehdizadeh Khalsaraei, An improvement on the positivity results for 2-stage explicit Runge- Kutta methods, J. Comput. Appl. Math., 235 (2010) 137-143.
4
[5] M. Mehdizadeh Khalsaraei, Positivity of an explicit Runge-Kutta method, Ain. Shams. Eng. J., 6(4) (2015) 1217-1223.
5
[6] M. Mehdizadeh Khalsaraei and F. Khodadosti, Nonstandard finite difference schemes for differential equations, Sahand. Commun. Math. Anal, 1(2) (2014) 47-54.
6
[7] M. Mehdizadeh Khalsaraei and R. Shokri Jahandizi, Positivity preserving schemes for Black-Scholes equation, Res. J. Fin. Account., 6(7) (2015) 101-105.
7
[8] M. Mehdizadeh Khalsaraei and R. Shokri Jahandizi, A modified explicit method for the Black-Scholes equation with positivity preserving property, J. Math. Comput. Sci., 15 (2015) 299-305.
8
[9] M. Mehdizadeh Khalsaraei and R. Shokri Jahandizi, Positivity preserving schemes with application to finance: option pricing, Appl. Math. Engin. Manage. Tech., 3(4) (2015) 212-220.
9
[10] M. Milev and A. Tagliani, Discrete monitored barrier options by finite difference schemes, Math. Edu. Math., 38 (2009) 81-89.
10
[11] M. Milev and A. Tagliani, Low volatility options and numerical diffusion of finite difference schemes, Serdica. Math. J., 36(3) (2010) 223-236.
11
[12] M. Milev and A. Tagliani, Nonstandard finite difference schemes with application to finance: option pricing, Serdica. Math. J., 36(1) (2010) 75-88.
12
[13] M. Milev and A. Tagliani, Numerical valuation of discrete double barrier options, J. Comput. Appl. Math., 233 (2010) 2468-2480.
13
[14] M. Milev and A. Tagliani, Efficient implicit scheme with positivity preserving and smoothing properties, J. Comput. Appl. Math., 243 (2013) 1-9.
14
[15] J.M. Ortega, Matrix Theory, Plenum Press, New York, 1988.
15
[16] J.M. Ortega, Numerical Analysis: a second course, Academic Press, New York, 1990.
16
[17] R. Rannacher, Finite element solution of diffusion problems with irregular data, Numer. Math., 43 (1984) 309-327.
17
[18] G.D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, 1985.
18
[19] D. Tavella and C. Randall, Pricing Financial Instruments: The Finite Difference Method, John Wiley and Sons, New York, 2000.
19
[20] B.A. Wade, A.Q.M. Khaliq, M. Yousuf, J. Vigo-Aguiar, and R. Deininger, On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options, J. Comput. Appl. Math., 204 (2007) 144--158.
20
[21] P. Wilmott, Derivatives: The Theory and Practice of Financial Engineering, John Wiley and Sons, Chichester, 1998.
21
[22] G. Windisch, M-Matrices in Numerical Analysis, in: Teubner-Texte Zur Mathematik, Leipzing, 1989.
22
ORIGINAL_ARTICLE
Latin-majorization and its linear preservers
In this paper we study the concept of Latin-majorizati-\\on. Geometrically this concept is different from other kinds of majorization in some aspects. Since the set of all $x$s Latin-majorized by a fixed $y$ is not convex, but, consists of union of finitely many convex sets. Next, we hint to linear preservers of Latin-majorization on $ \mathbb{R}^{n}$ and ${M_{n,m}}$.
http://scma.maragheh.ac.ir/article_22228_d8a2a927addcc6933428a2d0af4c0897.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
41
47
Doubly stochastic matrix
Latin-majorization
Latin square
Linear preserver
Mohammad Ali
Hadian Nadoshan
ma.hadiann@gmail.com
true
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
LEAD_AUTHOR
Hamid Reza
Afshin
afshin@vru.ac.ir
true
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Zip Code: 7718897111, Rafsanjan, Iran.
AUTHOR
[1] T. Ando, Majorization, doubly stochastic matrices, and comparision of eigenvalues, Linear Algebra Appl., 118 (1989) 163-248.
1
[2] A. Armandnejad and A. Salemi, The structure of linear preservers of gs-majorization, Bull. Iranian Math. Soc., 32 (2)(2006) 31-42.
2
[3] R. Bhatia, Matrix Analysis, Springer-Verlag, New York, 1997.
3
[4] G.H. Hardy, J.E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1988.
4
[5] A.M. Hasani and M. Radjabalipour, The structure of linear operators strongly preserving majorizations of matrices, Electronic Journal of Linear Algebra, 15 (2006) 260-268.
5
[6] F. Khalooei and A. Salemi, The Structure of linear preservers of left matrix majorization on ℝp, Electronic Journal of Linear Algebra, 18 (2009) 88-97.
6
[7] C.K. Li and E. Poon, Linear operators preserving directional majorization, Linear Algebra Appl., 325 (2001) 141-146.
7
[8] A.W. Marshall, I. Olkin, and B.C. Arnold, Inequalities: Theory of Majorization and Its Applications, Second Edition, Springer, New York, 2011.
8
[9] M. Niezgoda, Schur - Ostrowski type theorems revisited, J. Math. Anal. Appl., 381 (2) (2011) 935-946.
9
[10] J. Shao and W. Wei, A formula for the number of Latin squares, Discrete Mathematics, 110 (1992) 293-296.
10
ORIGINAL_ARTICLE
Symmetric module and Connes amenability
In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $\ell^1(S)$ is a symmetric $\ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigroup $E(S)$ of idempotents. In symmetric connes amenability, we have proved that $M(G)$ is symmetric connes amenable if and only if $G$ is amenable.
http://scma.maragheh.ac.ir/article_21382_4d0846371eaab14fedda80b8067ab743.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
49
59
Banach algebras
Symmetric amenability
Module amenability
Mohammad Hossein
Sattari
sattari@azaruniv.ac.ir
true
1
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
LEAD_AUTHOR
Hamid
Shafieasl
h.shafieasl@azaruniv.ac.ir
true
2
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
Department of Mathematics, Faculty of Science, Azarbaijan Shahid Madani University, P.O.Box 53751-71379, Tabriz, Iran.
AUTHOR
[1] M. Amini, Module Amenability for Semigroup Algebras, Semigroup Forum, 69 (2004), 243-254.
1
[2] J.F. Berglund, H.D. Junghenn, and P. Milnes, Analysis on Semigroups, Wiley–Interscience, New York, 1989.
2
[3] H.G. Dales, F. Ghahramani, and A.Ya. Helemskii, The amenability of measure algebras, J. London Math. Soc., 66 (2001), 213-226.
3
[4] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972).
4
[5] B.E. Johnson, Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. Proc. Camb. Phil. Soc., 120 (1996), 455-473.
5
[6] V. Runde, Connes-amenability and normal, virtual diagonals for measure algebras I, Bull. London Math. Soc. 47 (2015), 555-564.
6
[7] V. Runde, Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand. 95 (2004), 124 -144.
7
ORIGINAL_ARTICLE
Ozaki's conditions for general integral operator
Assume that $\mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $\mathcal{G}(\alpha)$ and $\mathcal{F}(\mu)$ as follows \begin{equation*} \mathcal{G}(\alpha):=\left\{f\in \mathcal{A}:\mathfrak{Re}\left( 1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\right) <1+\frac{\alpha }{2},\quad 0<\alpha\leq1\right\}, \end{equation*} and \begin{equation*} \mathcal{F}(\alpha):=\left\{f\in \mathcal{A}:\mathfrak{Re}\left( 1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\right) >\frac{1 }{2}-\mu,\quad -1/2<\mu\leq 1\right\}, \end{equation*} respectively, where $z \in \mathbb{D}$. In this paper, we study the mapping properties of this classes under general integral operator. We also, obtain some conditions for integral operator to be convex or starlike function.
http://scma.maragheh.ac.ir/article_17786_7cc766b7af9e228a4c99a78217ebf0de.pdf
2017-01-01T11:23:20
2017-11-19T11:23:20
61
67
Starlike function
Convex function
Locally univalent
Integral operator
Ozaki's conditions
Rahim
Kargar
rkargar1983@gmail.com
true
1
Department of Mathematics, Payame Noor University, I. R. of Iran.
Department of Mathematics, Payame Noor University, I. R. of Iran.
Department of Mathematics, Payame Noor University, I. R. of Iran.
LEAD_AUTHOR
Ali
Ebadian
ebadian.ali@gmail.com
true
2
Department of Mathematics, Payame Noor University, I. R. of Iran.
Department of Mathematics, Payame Noor University, I. R. of Iran.
Department of Mathematics, Payame Noor University, I. R. of Iran.
AUTHOR
[1] D. Breaz, M. Darus, and N. Breaz, Recent Studies on Univalent Integral Operators, Editure Aeternitas, Alba Iulia, 2010.
1
[2] D. Breaz, S. Owa, and N. Breaz, Some properties for general integral operators,Scientific Journal, 3 (2014) 9-14.
2
[3] D. Bshouty and A. Lyzzaik, Close-to-convexity criteria for planar harmonic mappings, Complex Anal. Oper. Theory, 5 (2011) 767-774.
3
[4] J.G. Clunie and T. Sheil-Small, Harmonic Univalent Functions, Ann. Acad. Sci. Fenn. Ser. A. I., 1984.
4
[5] P. Duren, Harmonic Mappings in the Plane, Cambridge Tracts in Mathematics. 156, Cambridge University Press, Cambridge, 2004.
5
[6] P. Duren, Univalent Functions (Grundlehren der mathematischen Wissenschaften 259), Springer, Berlin, 1983.
6
[7] A.W. Goodman, Univalent Functions, Vols. 1-2, Mariner, Tampa, Florida, 1983.
7
[8] P.T. Mocanu, Injective conditions in the complex plane, Complex Anal. Oper. Theory, {5} (2011) 759-786.
8
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