Circular symmetrization,subordination and arclength problems on convex functions |
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| Authors: | M Okada S Ponnusamy A Vasudevarao H Yanagihara |
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| Institution: | 1. Department of Applied Science, Faculty of Engineering, Yamaguchi University, Tokiwadai, Ube, Japan;2. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security),MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India;3. On leave from the Indian Institute ofTechnology Madras;4. Department of Mathematics, Indian Institute of Technology Kharagpur, West Bengal, India |
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| Abstract: | We study the class  of univalent analytic functions f in the unit disk  of the form  satisfying ![urn:x-wiley:0025584X:media:mana201500027:mana201500027-math-0004]( "urn:x-wiley:0025584X:media:mana201500027:mana201500027-math-0004") where Ω will be a proper subdomain of  which is starlike with respect to  . Let  be the unique conformal mapping of  onto Ω with  and  and  . Let  denote the arclength of the image of the circle  ,  . The first result in this paper is an inequality  for  , which solves the general extremal problem  , and contains many other well‐known results of the previous authors as special cases. Other results of this article cover another set of related problems about integral means in the general setting of the class  . |
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| Keywords: | Univalent close‐to‐convex starlike and convex functions integral means arclength symmetrization subordination 30C45 |
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