International Journal of Nonlinear Analysis and Applications

A new class of generalized convex functions and mathematical programming

Articles in Press

Document Type : Research Paper

Authors

1 Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

2 Department of Mathematics, Mahrah University, Al-Mahrah, Yemen

3 Department of Mathematics, Hadhramout University, Al-Mahrah, Yemen

4 Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl, 796012, Mizoram, India

10.22075/ijnaa.2024.32577.4848

Abstract

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.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 25 June 2024
  • Receive Date: 06 December 2023
  • Revise Date: 21 March 2024
  • Accept Date: 22 March 2024