TY - JOUR
A2 - Srivastava, Hari M.
AU - Devi, Satwanti
AU - Swaminathan, A.
PY - 2014
DA - 2014/07/01
TI - Integral Transforms of Functions to Be in a Class of Analytic Functions Using Duality Techniques
SP - 473069
VL - 2014
AB - Let Wβ(α,γ), 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-α+2γ)(f/z)+(α-2γ)f'+γzf″-β))>0, z∈D, for some ϕ∈R with α≥0, γ≥0, and β<1. Let M(ξ), 0≤ξ≤1, denote the Pascu class of ξ-convex functions given by the analytic condition Re((ξz(zf'(z))'+(1-ξ)zf'(z))/ (ξzf'(z)+(1-ξ)f(z)))>0 which unifies the classes of starlike and convex functions. The aim of this paper is to find conditions on λ(t) so that the integral transform of the form Vλ(f)(z)=∫01λ(t)(f(tz)/t)dtcarry functions from Wβ(α,γ) into M(ξ). As for the applications, for specific values of λ(t), it is found that several known integral operators carry functions from Wβ(α,γ) into M(ξ). The results for a more generalized operator related to Vλ(f)(z) are also given.
SN - 2314-4963
UR - https://doi.org/10.1155/2014/473069
DO - 10.1155/2014/473069
JF - Journal of Complex Analysis
PB - Hindawi Publishing Corporation
KW -
ER -