Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator

The motivation of the present article is to define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)<...

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Autores principales:	Abbas Kareem Wanas, Luminiţa-Ioana Cotîrlǎ
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	holormorphic function bi-univalent function upper bounds Fekete–Szegö functional (<i>p</i> − <i>q</i>)-Wanas operator Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c8b9e22eaab54606b13f3854a6e8d56c
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spelling	oai:doaj.org-article:c8b9e22eaab54606b13f3854a6e8d56c2021-11-25T19:06:53ZInitial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator10.3390/sym131121182073-8994https://doaj.org/article/c8b9e22eaab54606b13f3854a6e8d56c2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2118https://doaj.org/toc/2073-8994The motivation of the present article is to define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">A</mi><mi>E</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>ϑ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>E</mi></msub><mrow><mo>(</mo><mi>μ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>ϑ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> which are defined in the unit disk <i>U</i> associated with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Wanas operator. The upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö-type inequalities for the functions in these families are obtained. Furthermore, several consequences of our results are pointed out based on the various special choices of the involved parameters.Abbas Kareem WanasLuminiţa-Ioana CotîrlǎMDPI AGarticleholormorphic functionbi-univalent functionupper boundsFekete–Szegö functional(<i>p</i> − <i>q</i>)-Wanas operatorMathematicsQA1-939ENSymmetry, Vol 13, Iss 2118, p 2118 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	holormorphic function bi-univalent function upper bounds Fekete–Szegö functional (<i>p</i> − <i>q</i>)-Wanas operator Mathematics QA1-939
spellingShingle	holormorphic function bi-univalent function upper bounds Fekete–Szegö functional (<i>p</i> − <i>q</i>)-Wanas operator Mathematics QA1-939 Abbas Kareem Wanas Luminiţa-Ioana Cotîrlǎ Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
description	The motivation of the present article is to define the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">A</mi><mi>E</mi></msub><mrow><mo>(</mo><mi>λ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>ϑ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>E</mi></msub><mrow><mo>(</mo><mi>μ</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>;</mo><mi>ϑ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> which are defined in the unit disk <i>U</i> associated with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Wanas operator. The upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö-type inequalities for the functions in these families are obtained. Furthermore, several consequences of our results are pointed out based on the various special choices of the involved parameters.
format	article
author	Abbas Kareem Wanas Luminiţa-Ioana Cotîrlǎ
author_facet	Abbas Kareem Wanas Luminiţa-Ioana Cotîrlǎ
author_sort	Abbas Kareem Wanas
title	Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
title_short	Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
title_full	Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
title_fullStr	Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
title_full_unstemmed	Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator
title_sort	initial coefficient estimates and fekete–szegö inequalities for new families of bi-univalent functions governed by (<i>p</i> − <i>q</i>)-wanas operator
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c8b9e22eaab54606b13f3854a6e8d56c
work_keys_str_mv	AT abbaskareemwanas initialcoefficientestimatesandfeketeszegoinequalitiesfornewfamiliesofbiunivalentfunctionsgovernedbyipiiqiwanasoperator AT luminitaioanacotirla initialcoefficientestimatesandfeketeszegoinequalitiesfornewfamiliesofbiunivalentfunctionsgovernedbyipiiqiwanasoperator
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Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-Wanas Operator

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