Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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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)
  • Received : 2020.08.14
  • Accepted : 2021.04.10
  • Published : 2021.12.15
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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

Acknowledgement

The authors are thankful to the referees for their valuable comments and suggestions.

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