New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q -Srivastava-Attiya Operator

Abbas Kareem Wanas and Luminiţa-Ioana Cotîrlǎ
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Abbas Kareem Wanas: Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58801, Iraq
Luminiţa-Ioana Cotîrlǎ: Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 8, 1-9

Abstract: In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family J Σ ( λ , γ , s , t , q ; h ) of holomorphic and bi-univalent functions which were defined in the unit disk D associated with the q -Srivastava–Attiya operator. We establish the bounds for | a 2 | and | a 3 | , where a 2 , a 3 are the initial Taylor–Maclaurin coefficients. For the new family of functions J Σ ( λ , γ , s , t , q ; h ) we investigate the Fekete-Szegö inequality, special cases and consequences.

Keywords: holomorphic function; Bazilevi? function; bi-univalent function; Fekete–Szegö inequality; q-Srivastava–Attiya operator; upper bounds; Gegenbauer polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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