Some Results Related to Booth Lemniscate and Integral Operators

In this work, we explore the impact of integral operators such as the Libera and Alexander operators on specific families of analytic functions introduced in the literature and find some of their remarkable results. Using techniques from differential subordination and convolution theory, we establis...

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Main Authors: Bilal Khan, Zahra Orouji, Ali Ebadian
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Fractal and Fractional
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Online Access:https://www.mdpi.com/2504-3110/9/5/271
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author Bilal Khan
Zahra Orouji
Ali Ebadian
author_facet Bilal Khan
Zahra Orouji
Ali Ebadian
author_sort Bilal Khan
collection DOAJ
description In this work, we explore the impact of integral operators such as the Libera and Alexander operators on specific families of analytic functions introduced in the literature and find some of their remarkable results. Using techniques from differential subordination and convolution theory, we establish results concerning the radius of convexity and convolution properties for these function classes. Additionally, we investigate how these integral operators influence the geometric properties of functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">BS</mi><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">KS</mi><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, leading to new insights into their structural behavior.
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spelling doaj-art-7e6042d124e9415b967de31bbdaecc792025-08-20T03:14:39ZengMDPI AGFractal and Fractional2504-31102025-04-019527110.3390/fractalfract9050271Some Results Related to Booth Lemniscate and Integral OperatorsBilal Khan0Zahra Orouji1Ali Ebadian2Institute of Mathematics, Henan Academy of Sciences, No. 228, Chongshi Village, Zhengdong New District, Zhengzhou 450046, ChinaDepartment of Mathematics, Urmia University, Urmia 5756151818, IranDepartment of Mathematics, Urmia University, Urmia 5756151818, IranIn this work, we explore the impact of integral operators such as the Libera and Alexander operators on specific families of analytic functions introduced in the literature and find some of their remarkable results. Using techniques from differential subordination and convolution theory, we establish results concerning the radius of convexity and convolution properties for these function classes. Additionally, we investigate how these integral operators influence the geometric properties of functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">BS</mi><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">KS</mi><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, leading to new insights into their structural behavior.https://www.mdpi.com/2504-3110/9/5/271univalent functionsBooth lemniscateintegral operatorsdifferential subordination
spellingShingle Bilal Khan
Zahra Orouji
Ali Ebadian
Some Results Related to Booth Lemniscate and Integral Operators
Fractal and Fractional
univalent functions
Booth lemniscate
integral operators
differential subordination
title Some Results Related to Booth Lemniscate and Integral Operators
title_full Some Results Related to Booth Lemniscate and Integral Operators
title_fullStr Some Results Related to Booth Lemniscate and Integral Operators
title_full_unstemmed Some Results Related to Booth Lemniscate and Integral Operators
title_short Some Results Related to Booth Lemniscate and Integral Operators
title_sort some results related to booth lemniscate and integral operators
topic univalent functions
Booth lemniscate
integral operators
differential subordination
url https://www.mdpi.com/2504-3110/9/5/271
work_keys_str_mv AT bilalkhan someresultsrelatedtoboothlemniscateandintegraloperators
AT zahraorouji someresultsrelatedtoboothlemniscateandintegraloperators
AT aliebadian someresultsrelatedtoboothlemniscateandintegraloperators