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Integral transforms of functions to be in certain class defined by the combination of starlike and convex functions
, A. Swaminathan
Published in
2012
Volume: 63
   
Issue: 8
Pages: 1296 - 1304
Abstract
Let Pγ(β), β<1, denote the class of all normalized analytic functions f in the unit disc D=z∈C:|z|<1 such that Re( eiφ((1-γ)f(z)z+γ f′(z)-β)) >0,z∈D for some φ∈R. Let M(μ,α), 0≤μ<1, denote the Pascu class of α-convex functions of order μ and given by the analytic condition Reαz( zf′(z))′+(1-α) z f′(z)αz f′(z)+(1-α)f(z)>μ which unifies S*(μ) and C(μ), respectively, the classes of analytic functions that map D onto the starlike and convex domain. In this work, we consider integral transforms of the form Vλ(f)(z)= ∫01λ(t)f(tz)tdt. The aim of this paper is to find conditions on λ(t) so that the above transformation carry Pγ(β) into M(μ,α). As applications, for specific values of λ(t), it is found that several known integral operators carry Pγ(β) into M(μ,α). © 2012 Elsevier Ltd. All rights reserved.
About the journal
JournalComputers and Mathematics with Applications
ISSN08981221