<abstract xmlns="http://www.w3.org/1999/xhtml"> Let Wβδ(α,γ) be the class of normalized analytic functions f defined in the region |z| &lt; 1 and satisfying Re eiθ((1-α+2γ)(f/z)δ + (α-3γ+γ[(1-1/δ)(zf′/f) + 1/δ(1+zf″/f′)])(f/z)δ(zf′/f)-β)>0,with the conditions α ≤ 0, β &lt; 1, γ ≤ 0, δ > 0 φ ∈ ℝ. For a non-negative and real- valued integrable function λ(t) with ∫01 λ(t)dt = 1, the generalized non-linear integral transform is defined as Vλδ(f)(z) = (∫01λ(t)(f(tz)/t)δdt)1/δ.The main aim of the present work is to find conditions on the related parameters such that Vλδ(f)(z) ∈ Wβ1δ1(α1,γ1) whenever f ∈ Wβ2δ2(α2,γ2). Further, several interesting applications for specific choices of λ(t) are discussed. </abstract>

Let Wβδ(α,γ) be the class of normalized analytic functions f defined in the region |z| < 1 and satisfying Re eiθ((1-α+2γ)(f/z)δ + (α-3γ+γ[(1-1/δ)(zf′/f) + 1/δ(1+zf″/f′)])(f/z)δ(zf′/f)-β)>0,with the conditions α ≤ 0, β < 1, γ ≤ 0, δ > 0 φ ∈ ℝ. For a non-negative and real- valued integrable function λ(t) with ∫01 λ(t)dt = 1, the generalized non-linear integral transform is defined as Vλδ(f)(z) = (∫01λ(t)(f(tz)/t)δdt)1/δ.The main aim of the present work is to find conditions on the related parameters such that Vλδ(f)(z) ∈ Wβ1δ1(α1,γ1) whenever f ∈ Wβ2δ2(α2,γ2). Further, several interesting applications for specific choices of λ(t) are discussed.

Inclusion properties of Generalized Integral Transform using Duality Techniques

Department of Applied Sciences The NorthCap University, Sector 23-A Gurgaon, Haryana,

Department of Mathematics Indian Institute of Technology, Roorkee, Uttarkhand,

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Inclusion properties of Generalized Integral Transform using Duality Techniques"}

Let Wβδ(α,γ) be the class of normalized analytic functions f defined in the region |z| 0,with the conditions α ≤ 0, β  0 φ ∈ ℝ. For a non-negative and real- valued integrable function λ(t) with ∫01 λ(t)dt = 1, the generalized non-linear integral transform is defined as Vλδ(f)(z) = (∫01λ(t)(f(tz)/t)δdt)1/δ.The main aim of the present work is to find conditions on the related parameters such that Vλδ(f)(z) ∈ Wβ1δ1(α1,γ1) whenever f ∈ Wβ2δ2(α2,γ2). Further, several interesting applications for specific choices of λ(t) are discussed.

Let Wβδ(α,γ) be the class of normalized analytic functions f defined in the region |z| < 1 and satisfying Re eiθ((1-α+2γ)(f/z)δ + (α-3γ+γ[(1-1/δ)(zf′/f) +...

Inclusion properties of Generalized Integral Transform using Duality Techniques

Article Category: Research Article

Published Online: Feb 04, 2017

Page range: 91 - 106

Received: Feb 15, 2016

Accepted: Jun 16, 2016

DOI: https://doi.org/10.7603/s40956-016-0008-y

Keywords
Integral Transforms, Analytic functions, Hypergeometric functions, Convolution, Duality techniques

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Inclusion properties of Generalized Integral Transform using Duality Techniques

Article Category: Research Article

Published Online: Feb 04, 2017

Page range: 91 - 106

Received: Feb 15, 2016

Accepted: Jun 16, 2016

DOI: https://doi.org/10.7603/s40956-016-0008-y

KeywordsIntegral Transforms, Analytic functions, Hypergeometric functions, Convolution, Duality techniques

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Integral Transforms, Analytic functions, Hypergeometric functions, Convolution, Duality techniques