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

Abstract

In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family JΣ(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 |a2| and |a3|, where a2, a3 are the initial Taylor–Maclaurin coefficients. For the new family of functions JΣ(λ,γ,s,t,q;h) we investigate the Fekete-Szegö inequality, special cases and consequences.

Keywords

• holomorphic function
• Bazilevič function
• bi-univalent function
• Fekete–Szegö inequality
• q-Srivastava–Attiya operator
• upper bounds