2016
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A new sequence space and norm of certain matrix operators on this space
2
2
In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left sum_{j in {E_n}} x_j  sum_{j in E_{n + 1}} x_jright ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from $l_p$ into $ l_p(E,Delta)$, and apply our results to Copson and Hilbert matrices.
1

1
12


Hadi
Roopaei
Department of Mathematics, ValieAsr University of Rafsanjan, Rafsanjan, Iran.
Department of Mathematics, ValieAsr University
Iran
h.roopaei@gmail.com


Davoud
Foroutannia
Department of Mathematics, ValieAsr University of Rafsanjan,
Rafsanjan, Iran.
Department of Mathematics, ValieAsr University
Iran
foroutan@vru.ac.ir
Difference sequence space
Matrix domains
Norm
Copson matrix
Hilbert matrix
[[1] B. Altay and F. Basar, The ne spectrum and the matrix domain of the dierence operator Δ on the sequence space lp, (0 < p < 1), Commun. Math. Anal., 2(2) (2007) 111. ##[2] F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, ebooks, Monographs, Istanbul, 2012. ##[3] F. Basar and B. Altay, On the space of sequences of pbounded variation and related matrix mappings, Ukr. Math. J., 55(1) (2003) 136147. ##[4] F. Basar, B. Altay, and M. Mursaleen, Some generalizations of the space bvp of pbounded variation sequences, Nonlinear Anal., 68(2) (2008) 273287. ##[5] D. Foroutannia, On the block sequence space lp(E) and related matrix transfor mations, Turk. J. Math., 39 (2015) 830841. ##[6] D. Foroutannia, Upper bound and lower bound for matrix opwrators on weighted sequence spaces, Doctoral dissertation, Zahedan, 2007. ##[7] G.H. Hardy, J.E. Littlewood, and G. Polya, Inequalities, 2nd edition, Cambridge University press, Cambridge, 2001. ##[8] G.J.O. Jameson and R. Lashkaripour, Norms of certain operators on weighted lp spaces and Lorentz sequence spaces, J. Inequal. Pure Appl. Math., 3(1) (2002) Article 6. ##[9] H. Kizmaz, On certain sequence spaces I, Canad. Math. Bull., 25(2) (1981) 169176. ##[10] R. Lashkaripour and J. Fathi, Norms of matrix operators on bvp, J. Math. Inequal., 6(4) (2012) 589592. ##[11] M. Mursaleen and A.K. Noman, On some new dierence sequence spaces of nonabsolute type, Math. Comput. Modelling, 52 (2010) 603617. ##[12] H. Roopaei and D. Foroutannia, The norm of certain matrix operators on the new dierence sequence spaces, preprint.##]
The approximate solutions of Fredholm integral equations on Cantor sets within local fractional operators
2
2
In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools for solving local fractional integral equations.
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13
20


Hassan
Kamil Jassim
Department of Mathematics, Faculty of Education for Pure Sciences, University of ThiQar, Nasiriyah, Iraq.
Department of Mathematics, Faculty of Education
Iran
hassan.kamil28@yahoo.com
Fredholm integral equation
Local fractional Adomian decomposition method
Local fractional variational iteration method
[[1] H.K. Jassim, C. Unlu, S.P. Moshokoa, and C.M. Khalique, Local Fractional Laplace Variational Iteration Method for Solving Diusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015 Article ID 309870 (2015) 19. ##[2] S.S. Ray and P.K. Sahu, Numerical Methods for Solving Fredholm Integral Equations of Second Kind, Abstract and Applied Analysis, 2013 Article ID 42916 (2013)117. ##[3] C.T. Shieh and V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl., 347 (2008) 266272. ##[4] W.H. Su, D. Baleanu, X.J. Yang, and H. Jafari, Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method, Fixed Point Theory and Applications, 2013 Article 89 (2013) 17. ##[5] A.M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Springer, New York, NY, USA, 2011. ##[6] S.P. Yan, H. Jafari, and H.K. Jassim, Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014 Article ID 161580 (2014) 17. ##[7] Y.J. Yang, D. Baleanu, and X.J. Yang, A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis, 2013 Article ID 202650 (2013) 16. ##[8] Y.J. Yang, S.Q. Wang, and H.K. Jassim, Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014 Article ID 176395 (2014) 17. ##[9] X.J. Yang, D. Baleanu, and W.P. Zhong, Approximation solutions for diusion equation on Cantor timespace, Proceeding of the Romanian Academy, 14 (2013) 127133. ##[10] X.J. Yang, Local fractional integral equations and their applications, Advances in Computer Science and its Applications, 1 (2012) 234239. ##[11] X.J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012. ##[12] W.P. Zhong, F. Gao, X.M. Shen, Applications of YangFourier transform to local Fractional equations with local fractional derivative and local fractional integral operater, Adv. Mat. Res., 461 (2012) 306310.##]
Some properties of fuzzy real numbers
2
2
In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers.
In this study, we try to prove Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.
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27


Bayaz
Daraby
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science,
Iran
bdaraby@maragheh.ac.ir


Javad
Jafari
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science,
Iran
javad.jafari33333@gmail.com
Fuzzy real number
Bernoulli's inequality
Real number
[[1] T. Bag and S.K. Samanta, A comperative study of fuzzy norms on a linear space, Fuzzy Set and Systems, 159(6)(2008), 670684. ##[2] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems, 48 (1992), 239248. ##[3] M. Mizumoto and K. Tanaka, Some properties of fuzzy numbers, in: M.M. Gupta et al., Eds., Advances in Fuzzy Set Theory and Applications (NorthHolland, New York, 1979), 153164. ##[4] W. Rudin, Principles of Mathetical Analysis, McgrawHill, New York, 1976. ##[5] I. Sadeqi, F. Moradlou, and M. Salehi, On approximate Cauchy equation in Felbins type fuzzy normed linear spaces, to appear in Iran. J. Fuzzy Syst. 10: 3 (2013), 5163.##]
Some study on the growth properties of entire functions represented by vector valued Dirichlet series in the light of relative Ritt orders
2
2
For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of their relative Ritt order are the prime concern of this paper. Actually in this paper we establish some newly developed results related to the growth rates of entire functions on the basis of their relative Ritt order (respectively, relative Ritt lower order).
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35


Sanjib
Datta
Department of Mathematics, University of Kalyani, P.O.Kalyani, DistNadia, PIN 741235, West Bengal, India.
Department of Mathematics, University of
Iran
sanjib_kr_datta@yahoo.co.in


Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road, P.O.Krishnagar, DistNadia, PIN741101, West Bengal, India.
Rajbari, Rabindrapalli, R. N. Tagore Road,
Iran
tanmaybiswas_math@rediffmail.com


Pranab
Das
Department of Mathematics, University of Kalyani, P.O.Kalyani, DistNadia, PIN741235, West Bengal, India.
Department of Mathematics, University of
Iran
pranabdas90@gmail.com
Vector valued
Dirichlet series (VVDS)
Relative Ritt order
Relative Ritt lower order
Growth
[[1] Q.I. Rahaman, The Ritt order of the derivative of an entire function, Annales Polonici Mathematici., 17 (1965) 137140. ##[2] C.T. Rajagopal and A.R. Reddy, A note on entire functions represented by Dirichlet series, Annales Polonici Mathematici., 17 (1965) 199208. ##[3] J.F. Ritt, On certain points in the theory of Dirichlet series, Amer. Jour. Math., 50 (1928) 7386. ##[4] G.S. Srivastava, A note on relative type of entire functions represented by vector valued dirichlet series, Journal of Classicial Analysis, 2(1) (2013) 6172. ##[5] G.S. Srivastava and A. Sharma, On generalized order and generalized type of vector valued Dirichlet series of slow growth, Int. J. Math. Archive, 2(12) (2011) 26522659. ##[6] B.L. Srivastava, A study of spaces of certain classes of vector valued Dirichlet series, Thesis, I. I. T., Kanpur, 1983. ##[7] R.P. Srivastav and R.K. Ghosh, On entire functions represented by Dirichlet series, Annales Polonici Mathematici., 13 (1963) 93100.##]
Numerical solution of a class of nonlinear twodimensional integral equations using Bernoulli polynomials
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2
In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear twodimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficiency and accuracy of the method.
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51
سهراب
بزم
Sohrab
Bazm
Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Science,
Iran
sbazm@maragheh.ac.ir
Nonlinear twodimensional integral equations
Bernoulli polynomials
Collocation method
Operational matrices
[[1] E. Babolian, S. Bazm, and P. Lima, Numerical solution of nonlinear twodimensional integral equations using rationalized Haar functions, Commun. Nonl. Sci. Numer. Simul. 16(3) (2011) 1164{1175. ##[2] S. Bazm, Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations, J. Comput. Appl. Math. 275 (2015) 4460. ##[3] A. H. Bhrawy, E. Tohidi, and F. Soleymani, A new Bernoulli matrix method for solving highorder linear and nonlinear Fredholm integrodierential equations with piecewise intervals, Appl. Math. Comput. 219(2) (2012) 482497. ##[4] A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi, Higher Transcendental Functions, Vol. III, McGrawHill, New York, 1955. ##[5] H. Guoqiang, K. Hayami, K. Sugihara, and W. Jiong, Extrapolation method of iterated collocation solution for twodimensional nonlinear Volterra integral equations, App. Math. Comput. 112 (2009) 7076. ##[6] E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, 1989. ##[7] P. Lancaster, The Theory of Matrices: With Applications, second ed., Academic Press, New York, 1984. ##[8] Y.L. Luke, The Special Functions and Their Approximations, Vol. I, Academic Press, New York, 1969. ##[9] K. Maleknejad, S. Sohrabi, and B. Baranji, Application of 2DBPFs to nonlinear integral equations, Commun. Nonl. Sci. Numer. Simul. 15 (2010) 527535. ##[10] S. Nemati, P.M. Lima, and Y. Ordokhani, Numerical solution of a class of twodimensional nonlinear Volterra integral equations using Legendre polynomials, J. Comput. Appl. Math. 242 (2013) 53{69. ##[11] S. Nemati, and Y. Ordokhani, Solving Nonlinear TwoDimensional Volterra Integral Equations of the Firstkind Using the Bivariate Shifted Legendre Functions, International Journal of Mathematical Modelling & Computations 5(3)##(2015) 112. ##[12] A. Tari, M.Y. Rahimi, S. Shahmorad, and F. Talati, Solving a class of twodimensional linear and nonlinear Volterra integral equations by the dierential transform method, J. Comput. Appl. Math. 228 (2000) 4961. ##[13] F. Toutounian and E. Tohidi, A new Bernoulli matrix method for solving second order linear partial dierential equations with the convergence analysis, Appl. Math. Comput. 223 (2013) 298310.##]
On strongly Jordan zeroproduct preserving maps
2
2
In this paper, we give a characterization of strongly Jordan zeroproduct preserving maps on normed algebras as a generalization of Jordan zeroproduct preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zeroproduct preserving maps and strongly Jordan zeroproduct preserving maps are completely different. Also, we prove that the direct product and the composition of two strongly Jordan zeroproduct preserving maps are again strongly Jordan zeroproduct preserving maps. But this fact is not the case for tensor product of them in general. Finally, we prove that every $*$preserving linear map from a normed $*$algebra into a $C^*$algebra that strongly preserves Jordan zeroproducts is necessarily continuous.
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53
61


Ali Reza
Khoddami
Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161316, Shahrood, Iran.
Department of Pure Mathematics, University
Iran
khoddami.alireza@shahroodut.ac.ir
Strongly zeroproduct preserving map
Strongly Jordan zeroproduct preserving map
Zeroproduct preserving map
Jordan zeroproduct preserving map
Tensor product
[[1] M.A. Chebotar, W.F. Ke, P.H. Lee and N.C. Wong, Mappings preserving zero products , Studia Math., 155 1 (2003), 7794. ##[2] H. Ghahramani, Zero product determined triangular algebras , Linear Multilinear Algebra, 61 (2013), 741757. ##[3] A.R. Khoddami and H.R.E. Vishki, The higher duals of a Banach algebra induced by a bounded linear functional, Bull. Math. Anal. Appl. 3 (2011), 118122. ##[4] A.R. Khoddami, Strongly zeroproduct preserving maps on normed algebras induced by a bounded linear functional, Khayyam J. Math., 1 (2015), no. 1, 107114. ##[5] A.R. Khoddami, On maps preserving strongly zeroproducts, Chamchuri. J. Math., 7 (2015), 1623.##]
Parabolic starlike mappings of the unit ball $B^n$
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2
Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ and $z=(z_1,hat{z})in B^n$. In the case $gamma=1/2$, the function $Phi_{n,gamma}(f)$ reduces to the well known RoperSuffridge extension operator. By using different methods, we prove that if $f$ is parabolic starlike mapping on $U$ then $Phi_{n,gamma}(f)$ and $Psi_{n,beta}(f)$ are parabolic starlike mappings on $B^n$.
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63
70


Samira
Rahrovi
Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551761167, Bonab, Iran.
Department of Mathematics, Faculty of Basic
Iran
sarahrovi@gmail.com
RoperSuffridge extention operator
Biholomorphic mapping
Parabolic starlike function
[[1] I. Graham and G. Kohr, Univalent mappings associated with the RoperSuridge extension operator, J. Anal. Math., 81 (2000) 331342. ##[2] I. Graham and G. Kohr, An extension theorem and subclasses of univalent mappings in several complex variables, Complex Var., 47 (2002) 5972. ##[3] I. Graham and G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker, New York, (2003). ##[4] I. Graham, G. Kohr, and M. Kohr, Loewner chains and the RoperSuridge Extension Operator, J. Math. Anal. Appl., 247 (2000) 448465. ##[5] H. Hamad, T. Honda, and G. Kohr, Parabolic starlike mappings in Several complex variables, Manuscripta math. 123 (2007), 301324. ##[6] W. Hengartner and G. Schober, On schlicht mappings to domains convex in one direction, Comment. Math. Helv., 45 (1970), 303314. ##[7] J. A. Pfaltzgra and T.J. Suridge, An extension theorem and linear invariant families generated by starlike maps. Ann. Mariae Curie Sklodowska, 53 (1999), 193207. ##[8] K.A. Roper and T.J. Suridge, Convex mappings on the unit ball Cn, J. Anal. Math., 65 (1995), 333347. ##[9] T.J. Suridge, Starlike and convex maps in Banach spaces, Pac. J. Math., 46 (1973), 474489.##]