CERTAIN MULTIVALENT HARMONIC FUNCTION DEFINED BY GENERALIZED HYPERGEOMETRIC FUNCTIONS

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Published: 2017-07-01

Page: 177-188


VIMLESH KUMAR GUPTA *

Department of Mathematics & Astronomy, University of Lucknow, Lucknow, 226007 U.P., India.

*Author to whom correspondence should be addressed.


Abstract

In this paper, some multivalent harmonic functions F = H +∈ H (m) which are defined in terms of generalized hypergeometric functions are considered. Making use of coefficient inequalities for F ∈ H (m) satisfying some well known class conditions, we obtain the hypergeometric inequalities, which are sufficient for F to be in the classes S*H(mα),KH(m, α) and QH(m, α) and are necessary for the harmonic function F1  TH(m) ⊂ H (m). Further, some necessary and sufficient hypergeometric inequalities are given under some parametric restriction such that F ∈ TH(m). Results based on some integral operators are also given. A concluding remark based on special cases is mentioned.

Keywords: Multivalent harmonic starlike (convex) functions, generalized hypergeometric functions, gauss hypergeometric functions


How to Cite

GUPTA, V. K. (2017). CERTAIN MULTIVALENT HARMONIC FUNCTION DEFINED BY GENERALIZED HYPERGEOMETRIC FUNCTIONS. Asian Journal of Mathematics and Computer Research, 18(4), 177–188. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1071

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