On a subclass of β-uniformly convex functions defined by Dziok-Srivastava linear operator


  • Jamal M. Shenan




Dziok-Srivastava Linear operator, Hadamard product,


In this paper a new subclass of uniformly convex functions with negative coefficients defined by Dziok-Srivastava Linear operator is introduced. Characterization properties exhibited by certain fractional derivative operators of functions and the result of modified Hadmard product are discussed for this class. Further class preserving ntegral operator, extreme points and other interesting properties for this class are also indicated. 2000mathematics Subj. Classification: 30C45, 26A33.


A. Schild, On starlike functions of order α, Amer. J. Math. 87(1965), 65-70.

A. W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56(1991),87-92.

B. C.Carlson and D. B. Shaffer,Starlike and pre-starlike hypergeometric functions, SIAM J. Math. Anal. 15(1984),737-745.

D. Minda and W. Ma, Uniformly convex functions, Ann. Polon. Math. 57(1992),165-175.

F. Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118(1993),189-196.

G. Mur., T. Rosy and M. Darus, A subclass of uniformly convex functions associated with certain fractional calculus operators, J. Ineq. Pure and Appl. Math.,6(3) Art.,86(2005), 1-10.

H. Silverman, Univalent functions with negative coefficients, Proc Amer.

Math. Soc. 51(1975),109-116.

I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardly space of analytic functions associated with certain one-parameter families of integral transform, J. Math. Anal. Appl., 179(1993), 138-147.

J. Dziok and H. M. Srivastava, Certain subclass f analytic functions associated with the generalized hypergeometric function, Integral Transform Spec. funct., 14(2003), 7-18.

M. S. Robertson, On the theory of univalent functions, Ann. of Math.


R. K. Raina and M. Saigo, A note on fractional calculus operators

involving Fox’H-function on space Fp,μ , Recent Advances in Fractional

Calculus, Global Publishing Co. Sauk Rapids, 1993, pp. 219-229.

R. K. Raina and T. S. Nahar, Characterization properties for starlikeness and convexity of some subclasses of analytic functions involving a class of fractional derivative operator. Acta Math. Univ. Comenianae. Vol.LXIX,1(2000),1-8.

St. Ruscheweyh, New criteria for univalent functions, Proc. Amer.

Math. Soc., 49(1975), 109-115.

S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (5)(1987), 1057-1077.

Yu. E. Hohlov, Operators and operations in the class of univalent

functions, Izv. Vyss. Ucebn. Zaved. Mat., 10(1978), 83-89.