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Abstrakty
In this paper we introduce some subclasses of analytic functions with varying argument of coeffcients. These classes are defined in terms of the Hadamard product and generalize the well-known classes of uniformly convex functions. We investigate the coeffcients estimates, distortion properties, radii of starlikeness and convexity for defined classes of functions.
Czasopismo
Rocznik
Tom
Strony
13-26
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
autor
- Institute of Mathematics University of Rzeszów, ul. Rejtana 16A, 35-310 Rzeszów, Poland, jdziok@univ.rzeszow.pl
Bibliografia
- [1] P. Montel, Leçons sur les Fonctions Univalentes ou Multivalentes, Gauthier-Villars, Paris 1933.
- [2] H. Silverman, Univalent functions with varying arguments, Houston J. Math. 7(1981), 283-287.
- [3] H.M. Srivastava, S. Owa, Certain classes of analytic functions with varying arguments, J. Math. Anal. Appl. 136(1988), 217-228.
- [4] R.K Raina, D Bansal, Some properties of a new class of analytic functions defined in terms of a hadamard product, Journal of J. Ineq. Pure and Appl. Math. 9(2008), Article 22.
- [5] H.M. Srivastava, P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Ltd., Chichester), John Wiley and Sons, New York, Chichester, Brisbane and London 1985.
- [6] S. Owa, H.M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39(1987), 1057-1077.
- [7] C. Ramachandran, T.N. Shanmugam, H.M. Srivastava, A. Swaminathan, A unifed class of k-uniformly convex functions defined by the Dziok-Srivastava linear operator, Appl. Math. Comput. 190(2007), 1627-1636.
- [8] A.W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56(1991), 87-92.
- [9] W. Ma, D. Minda, Uniformly convex functions, Ann. Polon. Math. 57(1992), 165-175.
- [10] F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118(1993), 189-196.
- [11] J. Sokół, A. Wiśniowska, On some clasess of starlike functions related with parabola, Folia Sci. Univ. Tech. Resov. 121(1993), 35-42
- [12] S. Kanas, A. Wiśniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105(1999), 327-336.
- [13] S. Kanas, H.M. Srivastava, Linear operators associated with k-uniformaly convex functions, Intergral Transform and Spec. Funct. 9(2000), 121-132.
- [14] H.M. Srivastava, A.K. Mishra, Applications of fractional calculus to parabolic starlike and uniformly convex functions, Comput. Math. Appl. 39(2000), 57-69.
- [15] K.G. Subramanian, G. Murugusundaramoorthy, P. Balasubrahmanyam, H. Silverman, Subclasses of uniformly convex and uniformly starlike functions, Math. Japonica 42(1995), 517-522.
- [16] J. Dziok, Some properties of a new class of multivalent analytic functions, to appear
- [17] J. Dziok and H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct. 14 (2003), 7-18.
- [18] B.A. Frasin, Comprehensive family of uniformly analytic functions, Tamkang J. Math. 36(2005), 243-254.
- [19] H.M. Srivastava, G. Murugusundaramoorthy, S. Sivasubramanian, Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integral Transforms Spec. Funct. 18(2007), 511-52.
- [20] K. Vijaya, G. Murugusundaramoorthy, Some uniformly starlike functions with varying arguments, Tamkang J. Math. 35(2004), 23 -28.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA7-0043-0021