Existence results and two step proximal point algorithm for equilibrium problems on Hadamard manifolds

Abstract

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

Mixed Variational Inequality Interval-valued Problem: Theorems of Existence of Solutions

“…Remark 3.10. Hypothesis (c) extends to the case of interval-valued functions other similar ones that can be found in Theorem 3.2 given by Colao et al [9] and in Theorem 3.4 given by Al-Homidan et al [3].…”