The objective of the current paper is to incorporate new class and concepts convexity Hermite–Hadamard inequality with fuzzy Riemann integral operators because almost all classical single-valued interval-valued convex functions are special cases fuzzy-number valued mappings. Therefore, a nonconvex mapping in environment has been defined; up down h-pre-invex mappings (U.D F-N∙V∙Ms). With help th...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

Numerous applications of the theory convex and nonconvex mapping exist in fields applied mathematics engineering. In this paper, we have defined a new class functions which is known as up down pre-invex (pre-incave) fuzzy number valued mappings (F-N-V?Ms). The well-known Hermite–Hadamard (????????)-type related inequalities are taken into account work. We extend mileage further using Riemann in...