a new class of generalized convex functions and mathematical programming

In this paper, a new class of nonconvex optimization problem is considered, namely (h, φ)-(b, f, ρ)-convexity is defined for (h, φ)-differentiable mathematical programming problem. the sufficiency of the so-called karush-kuhn-tucker optimality conditions are established for the considered (h, φ)-differentiable mathematical programming problem under (generalized) (h, φ)-(b, f, ρ)-convexity hypotheses. further, the so-called mond-weir (h, φ)-dual problem is defined for the considered (h, φ)-differentiable mathematical programming problem and several duality theorems in the sense of mond-weir are derived under appropriate (generalized) (h, φ)-(b, f, ρ)-convex assumptions.