Fuzzy Mixed Variational-like and Integral Inequalities for Strongly Preinvex Fuzzy Mappings

It is a familiar fact that convex and non-convex fuzzy mappings play critical role in the study of optimization. Due to behavior its definition, idea convexity plays significant subject inequalities. The concepts symmetry have tight connection. We may use whatever we learn from one other, thanks correlation has developed between both recent years. Our aim consider new class (FMs) known as strongly preinvex (strongly preinvex-FMs) on invex set. These FMs are more general than (convex-FMs) (preinvex-FMs), when generalized differentiable (briefly, G-differentiable), preinvex-FMs invex-FMs). Some relationships among various established verified with support some useful examples. also shown optimality conditions G-differentiable functional, which sum non preinvex-FMs, can be distinguished by variational-like inequalities mixed inequalities, respectively. In end, strong relationship Hermite–Hadamard inequality preinvex-FM. Several exceptional cases discussed. very interesting outcome our main results appear ones. this research seen refinements improvements previously published findings.