In this paper, the author introduced the concept of generalized harmonically convex function on fractal sets Rα(0 < α 6 1) of real line numbers and established generalized Hermite-Hadamard’s inequalities for generalized harmonically convex function. Then, by creating a local fractional integral identity, obtained some Hermite-Hadamard type inequalities of these classes of functions. c ©2017 All...

in this paper, we study the convexity of the integral operator

In this paper we characterize nonsmooth convex vector functions by first and second order generalized derivatives. We also prove optimality conditions for convex vector problems involving nonsmooth data.

We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The prop...

In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator. Inclusion relationships for these subclasses are established. Also, we introduce some integral-preserving properties. Moreover, connections of the results presented here with those obtained in earlier works are poi...

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...