ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

doi:10.1016/S0252-9602(12)60108-8

Abstract

Abstract:

Making use of the Carlson–Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.

Key words: Hadamard product (or convolution), differential subordination, Carlson-Shaffer operator, k-starlike functions, k-uniformly convex function

CLC Number:

30C45

S. HUSSAIN, J. SOKóL. ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR[J].Acta mathematica scientia,Series B, 2012, 32(4): 1399-1407.

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