We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.
Abbas, M., Suleiman, Y., Vetro, C. (2017). A simulation function approach for best proximity point and variational inequality problems. MISKOLC MATHEMATICAL NOTES, 18(1), 3-16 [10.18514/MMN.2017.2015].
A simulation function approach for best proximity point and variational inequality problems
C. Vetro
2017-01-01
Abstract
We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.
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