Generalized scalar equilibrium problem with applications to best and coupled best approximations

摘要

In this paper, we present a new theorem on the existence of solutions for a three-function scalar equilibrium problem. Compactness is expressed in terms of the existence of feasibility sets of arbitrarily small measures of non-compactness, in addition to the completeness of the domain. Hereby we present some new results on the best approximations and coupled best approximations. We propose the generalized coupled coincidence problem and present a theorem on existence of its solution.