On generalized implicit operator equilibrium problems

On operator equilibrium problems

This paper is devoted to the study of operator equilibrium problems. By using the KKM theorem, we give sufficient conditions for the existence of solutions of these problems. As a consequence, the existence of solutions for operator variational inequalities and operator minimization problems are derived. AMS subject classifications: 49J45

On generalized implicit vector equilibrium problems in Banach spaces

Let X and Y be real Banach spaces, K be a nonempty convex subset of X , and C : K → 2Y be a multifunction such that for each u ∈ K , C(u) is a proper, closed and convex cone with intC(u) 6= ∅, where intC(u) denotes the interior of C(u). Given the mappings T : K → 2L(X,Y ,A : L(X, Y )→ L(X, Y ), f1 : L(X, Y )×K×K → Y , f2 : K×K → Y , and g : K → K , we introduce and consider the generalized impl...

On Generalized Implicit Vector Equilibrium Problems in Topological Ordered Spaces

Algorithm of Solutions for Solving Generalized Mixed Implicit Equilibrium Problems

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 ...

Generalized Nash Equilibrium Problems

The Generalized Nash equilibrium problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main properties and solution algorithms, pointing out what could be useful topics for future research in the field.