Some Inclusion Properties of New Subclass of Starlike and Convex Functions associated with Hohlov Operator

Janusz Sokól; Gangadharan Murugusundaramoorthy; Thilagavathi Kothandabani

doi:10.5666/KMJ.2016.56.2.597

Article

Kyungpook Mathematical Journal 2016; 56(2): 597-610

Published online June 1, 2016

Some Inclusion Properties of New Subclass of Starlike and Convex Functions associated with Hohlov Operator

Janusz Sokól¹, Gangadharan Murugusundaramoorthy², Thilagavathi Kothandabani²

Department of Mathematics, Rzesz´ow University of Technology, Al. Powsta´nc´ow Warszawy 12, 35-959 Rzesz´ow, Poland¹
School of advanced Sciences, VIT University, Vellore - 632014, India²

Received: March 7, 2014; Accepted: November 3, 2015

Abstract

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Abstract

For a sufficiently adequate special case of the Dziok-Srivastava linear operator defined by means of the Hadamard product (or convolution) with Srivastava-Wright convolution operator, the authors investigate several mapping properties involving various subclasses of analytic and univalent functions, G(λ, α) and M(λ, α). Furthermore we discuss some inclusion relations for these subclasses to be in the classes of k-uniformly convex and k-starlike functions.

Keywords: Srivastava-Wright convolution operator, ,Starlike functions, Convex functions, Uniformly Starlike functions, ,Uniformly Convex functions, Hadamard product, Hohlov operator, ,Gaussian hypergeometric ,function, Dziok-Srivasta