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 ...

The goal of this study is to create new variations the well-known Hermite–Hadamard inequality (HH-inequality) for preinvex interval-valued functions (preinvex I-V-Fs). We develop several additional inequalities class whose product I-V-Fs. findings described here would be generalizations those found in previous studies. Finally, we obtain Hermite–Hadamard–Fejér with support functions. Some and c...

A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-Epreinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic proper...

Keywords--Fuzzy numbers, Convexity, Preinvexity, Generalized convexity, Fuzzy mappings. 1. I N T R O D U C T I O N Let R n deno te t he n -d imens iona l Euc l idean space. T h e suppor t , supp (p), of a fuzzy set # : R n ~ I = [0, 1] is def ined as s u p p ( # ) = { x e R n ] # ( x ) > 0} . A fuzzy set # : R n ~ I is cal led fuzzy convex if i t is quas i concave in c o m m o n sense on its su...