Higher-Order Mond-Weir Duality of Set-Valued Fractional Minimax Programming Problems

Abstract

In this paper, we consider a set-valued fractional minimax programming problem (abbreviated as SVFMPP) (MFP), in which both the objective and constraint maps are set-valued. We use the concept of higher-order α-cone arcwisely connectivity, introduced by Das [1], as a generalization of higher-order cone arcwisely connected setvalued maps. We explore the higher-order Mond-Weir (MWD) form of duality based on the supposition of higher-order α-cone arcwisely connectivity and prove the associated higher-order converse, strong, and weak theorems of duality between the primary (MFP) and the analogous dual problem (MWD).