By using the q-derivative operator and Legendre polynomials, some new subclasses of q-starlike functions bi-univalent are introduced. Several coefficient estimates Fekete–Szegö-type inequalities for in each these obtained. The results derived this article shown to extend generalize those earlier works.

A class of p-valent analytic functions is introduced using the q-difference operator and familiar Janowski functions. Several properties in class, such as Fekete–Szegö inequality, coefficient estimates, necessary sufficient conditions, distortion growth theorems, radii convexity starlikeness, closure theorems partial sums, are discussed this paper.

Three subclasses of analytic and bi-univalent functions are introduced through the use q?Gegenbauer polynomials, which a generalization Gegenbauer polynomials. For falling within these subclasses, coefficient bounds a2 a3 as well Fekete–Szegö inequalities derived. Specializing parameters used in our main results leads to number new results.

In the present paper, we aimed to discuss certain coefficient-related problems for inverse functions associated with a bounded turning class subordinated exponential function. We calculated bounds of some initial coefficients, Fekete–Szegö-type inequality, and estimation Hankel determinants second third order. All these were proven be sharp.

Using $ (p, q) $-Lucas polynomials and bi-Bazilevic type functions of order $\rho +i\xi,$ we defined a new subclass biunivalent functions. We obtained coefficient inequalities for belonging to the subclass. In addition these results, upper bound Fekete-Szegö functional was obtained. Finally, some special values parameters, several corollaries were presented.

The purpose of this article is to obtain the sharp estimates first four initial logarithmic coefficients for class BTs bounded turning functions associated with a petal-shaped domain. Further, we investigate estimate Fekete-Szegö inequality, Zalcman inequality on and Hankel determinant H2,1Ff/2 H2,2Ff/2 entry coefficients.

The present paper introduces a new class of bi-univalent functions defined on symmetric domain using Gegenbauer polynomials. For in this class, we have derived the estimates Taylor–Maclaurin coefficients, a2 and a3, Fekete-Szegö functional. Several results follow upon specializing parameters involved our main results.

For the first time, we attempted to define two new sub-classes of bi-univalent functions in open unit disc complex order involving Mathieu-type series, associated with generalized telephone numbers. The initial coefficients these classes were obtained. Moreover, also determined Fekete–Szegö inequalities for function and several related corollaries.

In this article, we use the q-derivative operator and principle of subordination to define a new subclass analytic functions related q-Ruscheweyh operator. Sufficient conditions, sharp bounds for initial coefficients, Fekete–Szegö functional Toeplitz determinant are investigated class functions. Additionally, also present several established consequences derived from our primary findings.