On an Integral Transform of a Class of Analytic Functions

For and , let denote the class of all normalized analytic functions in the open unit disc such that , for some . It is known (Noshiro (1934) and Warschawski (1935)) that functions in are close-to-convex and hence univalent for . For , we consider the integral transform , where is a nonneg...

Full description

Saved in:
Bibliographic Details
Main Authors: Sarika Verma, Sushma Gupta, Sukhjit Singh
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/259054
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850224261402198016
author Sarika Verma
Sushma Gupta
Sukhjit Singh
author_facet Sarika Verma
Sushma Gupta
Sukhjit Singh
author_sort Sarika Verma
collection DOAJ
description For and , let denote the class of all normalized analytic functions in the open unit disc such that , for some . It is known (Noshiro (1934) and Warschawski (1935)) that functions in are close-to-convex and hence univalent for . For , we consider the integral transform , where is a nonnegative real-valued integrable function satisfying the condition . The aim of present paper is, for given , to find sharp values of such that (i) whenever and (ii) whenever .
format Article
id doaj-art-51d3fb5cb31d4cc0b122001cd04140de
institution OA Journals
issn 1085-3375
1687-0409
language English
publishDate 2012-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-51d3fb5cb31d4cc0b122001cd04140de2025-08-20T02:05:41ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/259054259054On an Integral Transform of a Class of Analytic FunctionsSarika Verma0Sushma Gupta1Sukhjit Singh2Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal 148106, IndiaFor and , let denote the class of all normalized analytic functions in the open unit disc such that , for some . It is known (Noshiro (1934) and Warschawski (1935)) that functions in are close-to-convex and hence univalent for . For , we consider the integral transform , where is a nonnegative real-valued integrable function satisfying the condition . The aim of present paper is, for given , to find sharp values of such that (i) whenever and (ii) whenever .http://dx.doi.org/10.1155/2012/259054
spellingShingle Sarika Verma
Sushma Gupta
Sukhjit Singh
On an Integral Transform of a Class of Analytic Functions
Abstract and Applied Analysis
title On an Integral Transform of a Class of Analytic Functions
title_full On an Integral Transform of a Class of Analytic Functions
title_fullStr On an Integral Transform of a Class of Analytic Functions
title_full_unstemmed On an Integral Transform of a Class of Analytic Functions
title_short On an Integral Transform of a Class of Analytic Functions
title_sort on an integral transform of a class of analytic functions
url http://dx.doi.org/10.1155/2012/259054
work_keys_str_mv AT sarikaverma onanintegraltransformofaclassofanalyticfunctions
AT sushmagupta onanintegraltransformofaclassofanalyticfunctions
AT sukhjitsingh onanintegraltransformofaclassofanalyticfunctions