In a recent paper [14], the fixed point and resolvent techniques have been used to give an iterative algorithm for solving generalized mixed equilibrium problem (GMEP). In this paper, an extended iterative algorithm, called generalized mean proximal algorithm (GMPA) is presented and its convergence to the solution of GMEP with θ-pseudomonotne and δLipschitz continuous mappings in Hilbert spaces...

We propose a hybrid decision-making framework for safe and efficient autonomous driving of selfish vehicles on highways. Specifically, we model the dynamics of each vehicle as a Mixed-Logical-Dynamical system and propose simple driving rules to prevent potential sources of conflict among neighboring vehicles. We formalize the coordination problem as a generalized mixed-integer potential game, w...

The purpose of this paper is to introduce a new generalized system of nonlinear quasi-mixed equilibrium problems and find the common solutions of this problem and a fixed point problem. The results obtained in this paper may be viewed as an extension, refinement and improvement of the previously known results in [2-4] and others. Mathematics Subject Classification: 47H09, 47J25

Inspired by the optimal value approach, we propose a new reformulation of the optimistic Bilevel programming Problem (BP) as a suitable Generalized Nash Equilibrium Problem (GNEP). We provide a complete analysis of the relationship between the original hierarchical BP and the corresponding “more democratic” GNEP. Moreover, we investigate solvability and convexity issues of our reformulation. Fi...

In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems i...

A new system of generalized mixed implicit equilibrium problems is introduced and studied in real reflexive Banach space. A system of generalized equation problems is considered and its equivalence with the system of generalized mixed implicit equilibrium problems is shown. The iterative algorithm of the solutions is constructed and analyzed through a fixed point formulation of the generalized ...

The purpose of this paper is to investigate nonemptyness of the solution set for generalized mixed quasi-equilibrium problems and investigate the asymptotic behavior of an iterative algorithm for finding common solution of generalized mixed equilibrium problems and fixed point problems of asymptotically nonexpansive mappings under mild conditions of iteration parameters. Our results improve and...