Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 16 5 2025 05 01 A new class of generalized convex functions and mathematical programming 153 164 8781 10.22075/ijnaa.2024.32577.4848 EN Najeeb Abdulaleem Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland Department of Mathematics, Mahrah University, Al-Mahrah, Yemen Department of Mathematics, Hadhramout University, Al-Mahrah, Yemen Solomon Lalmalsawma Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl, 796012, Mizoram, India Vinay Singh Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl, 796012, Mizoram, India Journal Article 2023 12 06 In this paper, a new class of nonconvex optimization problem is considered, namely  $(h,\varphi)$-$(b,F,\rho)$-convexity is defined for $(h,\varphi)$-differentiable mathematical programming problem. The sufficiency of the so-called Karush-Kuhn-Tucker optimality conditions are established for the considered $(h,\varphi)$-differentiable mathematical programming problem under (generalized) $(h,\varphi)$-$(b,F,\rho)$-convexity hypotheses. Further, the so-called  Mond-Weir $(h,\varphi)$-dual problem is defined for the considered $(h,\varphi)$-differentiable mathematical programming problem and several duality theorems in the sense of Mond-Weir are derived under appropriate (generalized) $(h,\varphi)$-$(b,F,\rho)$-convex assumptions. https://ijnaa.semnan.ac.ir/article_8781_73edb15a2775f8a901a13581eeb776fa.pdf