Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-28T10:23:19.811Z Has data issue: false hasContentIssue false
  • English
  • Français

Applications of differential subordinations for norm estimates of an integral operator

Part of: Geometric function theory

Published online by Cambridge University Press:  06 November 2017

Jacek Dziok ,
Ravinder Krishna Raina  and
Janusz Sokół
Jacek Dziok
Affiliation:
University of Rzeszów, Faculty of Mathematics and Natural Sciences, ul. Prof. Pigonia 1, 35–310 Rzeszów, Poland (jdziok@univ.rzeszow.pl)
Ravinder Krishna Raina
Affiliation:
Maharana Pratap University of Agriculture and Technology, Udaipur, India
Janusz Sokół
Affiliation:
University of Rzeszów, Faculty of Mathematics and Natural Sciences, ul. Prof. Pigonia 1, 35–310 Rzeszów, Poland (jsokol@prz.edu.pl)
Get access Rights & Permissions [Opens in a new window]

Abstract

By considering the norm of a locally univalent function given by

we obtain such norm estimates for an operator of functions involving a convolution structure of convex univalent functions with a subclass of convex functions (defined by subordination). We also obtain some inequalities concerning this norm for functions under a certain fractional integral operator. Some implications of our results are briefly pointed out in the concluding section.

Keywords

norm estimatesunivalent functionsstar-like functionssubordinationfractional integral operator

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 2 , April 2018 , pp. 281 - 291
Copyright
Copyright © Royal Society of Edinburgh 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)