The purpose of this article is to introduce a new subclass analytic and bi-univalent functions, in associated with sigmoid function investigate the upper bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Further we obtain Fekete-Szego inequalities class sigma. We also give several illustrative examples functionclass which here.

In this present investigation, the authors obtain Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which zf ′(z) (1− λ)f(z) + λzf ′(z) (0 ≤ λ < 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are giv...

This article defines a new operator called the q-Babalola convolution by using quantum calculus and of normalized analytic functions in open unit disk. We then study class bi-univalent defined disk associated with operator. The main results investigation include some upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szego inequalities class. Many applications finds are highlighted c...

Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in open unit disk $\mathbb{U}$ and given by\[f(z)=z+\sum_{n=2}^{\infty }a_{n}z^{n}\qquad \left( z\in \mathbb{U}\right) .\]The coefficient functional $\phi _{\lambda }\left( f\right) =a_{3}-\lambda a_{2}^{2}$ on $f\in \mathcal{A}$ represents various geometric quantities. For example, _{1}\left( =a_{3}-a_{2}^{2}=S_{f}\left( 0\...

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) \(k\)-Fibonacci numbers. We derive bounds on initial coefficients Fekete-Szego functional for \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, in...

In this present investigation, the authors obtain a sharp Fekete-Szegö’s inequality for certain normalized analytic functions f(z) defined on the open unit disk for which (1 + β) ( z f(z) )α − βf ′(z) ( z f(z) )1+α , (β ∈ C, 0 < α < 1) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also, certain applications of our results for a class of functions de...

In this paper we obtain the Fekete-Szegö inequality for a class of analytic functions f(z) defined in the open unit disk for which

to general mean values of the form fli\f(x)\dx, p^l} Hille, Szego and Tamarkin [ l ] 1 gave three proofs of the inequality (1), two products of the general case of exponent p, and another for the case £ = 2, stated by the authors to be similar to the original unpublished proof of Schmidt. It seems worthwhile tó sketch a short elementary proof of the important case p = 2, depending only upon an ...