AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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Authors: LATEEF AHMAD WANI, SWAMINATHAN ANBHU.
DOI: 10.24193/subbmath.2020.2.04
Published Online: 2020-06-05
Published Print: 2020-06-30
pp. 211-227
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ABSTRACT: In this work, conditions on the parameters $a, b$ and $c$ are given so that the normalized Gaussian hypergeometric function $zF(a,b;c;z)$, where F(a,b;c;z)=∑n=0∞(a)n(b)n(c)n(1)nzn,|z|<1, is in certain class of analytic functions. Using Taylor coefficients of functions in certain classes, inclusion properties of the Hohlov integral transform involving $zF(a,b;c;z)$ are obtained. Similar inclusion results of the Komatu integral operator related to the generalized polylogarithm are also obtained. Various results for the particular values of these parameters are deduced and compared with the existing literature.
Key words: Univalent; Convex; Starlike; Close-to-convex functions, Gaussian hypergeometric functions, Incomplete beta functions, Komatu integral operator, Polylogarithm
