"In this paper, we introduce new class $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$ of $m$-fold symmetric bi-univalent functions. Furthermore, use the Faber polynomial expansions to find upper bounds for general coefficients $|a_{mk+1}|(k \geqq 2)$ functions in $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$. Moreover, obtain estimates initial $|a_{m+1}| $ and $|a_{2m+1}|$ class. The results presented paper w...

The objective of this paper is to define and study further generalization of extended gamma, extended beta and extended hypergeometric functions. Closed form representation of the generalized extended gamma function is derived in the form of Meijer’s G-function. Some of their properties and special cases are also derived. These functions have applications in probability theory, reliability, ast...

In this present paper, the main aim of the authors are to present extended k-gamma, k-beta functions and extended k-beta distribution where k > 0. These newly defined functions are the generalized forms of the extended gamma, beta functions and extended beta distribution. Also, we further generalize the said functions and some of their properties.

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning clas...

‎In this paper‎, ‎using a generalized translation operator‎, ‎we obtain a generalization of Younis Theorem 5.2 in [3] for the Cherednik-Opdam transform for functions satisfying the $(delta,gamma,p)$-Cherednik-Opdam Lipschitz condition in the space‎ ‎$L^{p}_{alpha,beta}(mathbb{R})$.