Non-differentiable minimax fractional programming with generalized α-univexity

In this paper, we study a non-differentiable minimax fractional programming problem under the assumption of generalized α-univex function. In this paper we extend the concept of α-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo α-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75] to α-univexity and pseudo α-univexity from a view point of generalized convexity. We also introduce the concept of strict pseudo α-univex and quasi α-univex functions. We derive Karush-Kuhn-Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different form of dual problems. The results in this paper extend a few known results in the literature.