Integral Transforms of Functions to Be in a Class of Analytic Functions Using Duality Techniques
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-01
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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)dt carry 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.
American Psychological Association (APA)
Devi, Satwanti& Swaminathan, A.. 2014. Integral Transforms of Functions to Be in a Class of Analytic Functions Using Duality Techniques. Journal of Complex Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-474286
Modern Language Association (MLA)
Devi, Satwanti& Swaminathan, A.. Integral Transforms of Functions to Be in a Class of Analytic Functions Using Duality Techniques. Journal of Complex Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-474286
American Medical Association (AMA)
Devi, Satwanti& Swaminathan, A.. Integral Transforms of Functions to Be in a Class of Analytic Functions Using Duality Techniques. Journal of Complex Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-474286
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-474286