Equilibrium problems with generalized relaxed monotonicities in Banach spaces

Existence Results for Some Equilibrium Problems Involvingα-Monotone Bifunction

“…Therefore, ∈ is a solution of problem (9). Conversely, assume that ∈ is a solution of problem (9) and fix ∈ .…”

“…In recent years, a number of authors have proposed many essential generalizations of monotonicity, such as -monotonicity, relaxed monotonicity, relaxed -monotonicity, and quasimonotonicity (see [7][8][9][10]). …”

Iterative Algorithm for extended mixed equilibrium problem

“…It has been shown that the equilibrium problem provides a natural, novel and unified framework to study a wide class of problems arising in nonlinear analysis, optimization, economics, finance and game theory. The equilibrium problem includes many mathematical problems as particular cases such as mathematical programming problems, complementarity problem, variational inequality problems, fixed point problems, minimax inequality problems, Nash equilibrium problems in non-cooperative games, etc., see [1,2,4,6,11].…”

On the existence of solutions of generalized equilibrium problems with α−β−η -monotone mappings

“…The most important application of generalized equilibrium problems is in economics [1,3], variational inequalities [5], optimization, fixed point theory [6] and so on. Over the last few years, the concept of generalized equilibrium problems has been studied by various authors and has developed rapidly (see [2,13,14,17,18]). Onjai-uea and his colleagues in [15] presented a relaxed hybrid steepest method to find a common element for the set of fixed points of a nonexpansive mapping, the set of solutions of a variational inequality for an inverse-strongly monotone mapping and the set of solutions of generalized mixed equilibrium problems in Hilbert spaces.…”