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On a class of difference operator and its applications to a family of analytic functions

Part of: Special classes of linear operators Geometric function theory

Published online by Cambridge University Press:  27 February 2023

Ravinder Krishna Raina ,
Janusz Sokół Open the ORCID record for Janusz Sokół [Opens in a new window]  and
Katarzyna Tra̧bka-Wiȩcław
Ravinder Krishna Raina
Affiliation:
M.P., University of Agriculture and Technology, Udaipur 313001, Rajasthan, India (rkraina_7@hotmail.com)
Janusz Sokół
Affiliation:
University of Rzeszów, College of Natural Sciences, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland (jsokol@ur.edu.pl, jsokol@prz.edu.pl)
Katarzyna Tra̧bka-Wiȩcław
Affiliation:
Lublin University of Technology, Mechanical Engineering Faculty, ul. Nadbystrzycka 36, 20-618 Lublin, Poland (k.trabka@pollub.pl)
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Abstract

This paper mainly considers the problem of generalizing a certain class of analytic functions by means of a class of difference operators. We consider some relations between starlike or convex functions and functions belonging to such classes. Some other useful properties of these classes are also considered.

Keywords

q-calculusp,q-difference operatorq-derivativeanalytic functionsq-starlike functions

MSC classification

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C50: Coefficient problems for univalent and multivalent functions 47B99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 1 , February 2024 , pp. 248 - 258
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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Footnotes

*

Present address: 10/11 Ganpati Vihar, Opposite Sector 5, Udaipur 313002, Rajasthan, India.

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