The study of the q-analogue classical results geometric function theory is currently great interest to scholars. In this article, we define generalized classes close-to-convex functions and quasi-convex with help q-difference operator. Moreover, by using q-analogues a certain family linear operators, Kq,bsh, K˜q,sbh, Qq,bsh, Q˜q,sbh are introduced. Several interesting inclusion relationships be...

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

The object of this paper to derive certain sucient condi-tions for close-to-convexity of certain analytic functions dened on theunit disk  

in this work, we obtain the fekete-szegö inequalities for the class $p_{sigma }left( lambda ,phi right) $ of bi-univalent functions. the results presented in this paper improve the recent work of prema and keerthi [11].