The notions of a quasi-monotone operator and of a cyclically quasi-monotone operator are introduced, and relations between such operators and quasi-convex functions are established.

A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety classes convexities, is presented. In the various convexities this includes classical convex functions, quasi-convex p-convex (p,s)-convex modified (p,h)-convex tgs-convex η-quasi-convex ϕ-convex (α,m)-convex ϕ-quasi-convex and coordinated functions. Quantum H-H via preinvex functions ...

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 and the differential subordination principle. Inclusion relationships for these subclasses are established. Moreover, we introduce some integral-preserving properties. Key-Words: Starlike function; Convex function; ...

The aim of this paper is to characterize in terms of classical (quasi)convexity of extended real-valued functions the set-valued maps which are K-(quasi)convex with respect to a convex cone K. In particular, we recover some known characterizations of K-(quasi)convex vector-valued functions, given by means of the polar cone of K.

‎The proximal point algorithm‎, ‎which is a well-known tool for finding‎ ‎minima of convex functions‎, ‎is generalized from the classical‎ ‎Hilbert space framework into a nonlinear setting‎, ‎namely‎, ‎geodesic‎ ‎metric spaces of nonpositive curvature‎. ‎In this paper we propose an‎  ‎iterative algorithm for finding the common element of the‎ ‎minimizers of a finite family of convex functions a...