Analytic Functions of Complex Order Defined by Fractional Integrals Involving Fox\'s H-functions

K  Uma; G  Murugusundaramoorthy and K  Vijaya

doi:10.17485/ijst/2015/v8i16/52222

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Analytic Functions of Complex Order Defined by Fractional Integrals Involving Fox's H-functions

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i16/52222

Year: 2015, Volume: 8, Issue: 16, Pages: 1-7

Original Article

Analytic Functions of Complex Order Defined by Fractional Integrals Involving Fox's H-functions

K. Uma^* , G. Murugusundaramoorthy and K. Vijaya

School of Advanced Sciences, VIT University, Vellore - 632014, Tamil Nadu, India;
[email protected], [email protected], [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

We introduced certain new subclasses of analytic functions of complex order defined by fractional integrals involving Fox’s H-functions in the unit disc and investigate the various properties and characteristics of analytic functions belonging to the subclasses Sn (l,b,g). We also defined an another subclass Rn (l,b,g) involving Fox’s H- functions. Apart from deriving a set of coefficient bounds for each of these function classes, we establish several inclusion relationships involving the (n, d) — neighbourhoods of analytic functions with negative coefficients belonging to these subclasses.
Keywords: Convex, Generalized Hypergeometric Functions, Hadamard Product, Inclusion Relations, (n, d)-Neighborhood, Starlike, Univalent