Abstract
We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.
Highlights
A continuous function f = u + iv is a complex-valued harmonic function in a complex domain G if both u and v are real and harmonic in G
We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc
M 2 m 1 where the analytic functions h and g are in the forms h(z) z am zm, g(z) bm zm (| b1 | 1)
Summary
From (8) we define, Wright generalized hypergeometric harmonic function f h g of the form (1), as. For 0 1, let WSH ([ 1], ) denote the subfamily of starlike harmonic functions f H of the form (1). In this paper we obtain a sufficient coefficient condition for functions f given by (2) to be in the class WSH ([ 1], ). We begin deriving a sufficient coefficient condition for the functions belonging to the class WSH ([ 1], ). We conclude that it is both necessary and sufficient that the coefficient bound inequality (17) holds true when f WVH ([ 1], ). This completes the proof of Theorem 2.
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