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http://dx.doi.org/10.22771/nfaa.2021.26.05.02

A GENERALIZED CLASS OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH AL-OBOUDI OPERATOR INVOLVING CONVOLUTION  

Sangle, N.D. (Department of Mathematics, D.Y. Patil College of Engineering and Technology)
Metkari, A.N. (Research Scholar Department of Mathematics, Visvesvaraya Technological University)
Joshi, S.B. (Department of Mathematics, Walchand College of Engineering)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.5, 2021 , pp. 887-902 More about this Journal
Abstract
In this paper, we have introduced a generalized class SiH (m, n, 𝛾, 𝜙, 𝜓; 𝛼), i ∈ {0, 1} of harmonic univalent functions in unit disc 𝕌, a sufficient coefficient condition for the normalized harmonic function in this class is obtained. It is also shown that this coefficient condition is necessary for its subclass 𝒯 SiH (m, n, 𝛾, 𝜙, 𝜓; 𝛼). We further obtained extreme points, bounds and a covering result for the class 𝒯 SiH (m, n, 𝛾, 𝜙, 𝜓; 𝛼). Also, show that this class is closed under convolution and convex combination. While proving our results, certain conditions related to the coefficients of 𝜙 and 𝜓 are considered, which lead to various well-known results.
Keywords
Harmonic functions; univalent functions; convolution; Al-Oboudi operator;
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Times Cited By KSCI : 1  (Citation Analysis)
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