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In this paper, We improve several results recently established by Rehman et al. [14] for the gamma and beta k-functions by using some classical inequalities like Chebychev, Hölder and Grüss inequalities. [ABSTRACT FROM AUTHOR]

Mubeen [5] has recently introduced the second order linear differential equations of k-hypergeometric and con uent k-hypergeometric functions. The main objective of this present paper is to develop these k-hypergeometric and con uent k-hypergeometric differential equations by adopting the same method, used by Rainville in [6]. Also, we find out the solutions of the form w =2 F1,k ((α, k); (β, k); (γ, k); z) and w =1 F1,k ((α, k); (β, k); z) of k- hypergeometric and con uent k-hypergeometric differential equations respectively, in the same way. [ABSTRACT FROM AUTHOR]