We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.
Tchier, F., Vetro, C., Vetro, F. (2016). Best approximation and variational inequality problems involving a simulation function. FIXED POINT THEORY AND APPLICATIONS, 2016(1), 1-15 [10.1186/s13663-016-0512-9].
Best approximation and variational inequality problems involving a simulation function
VETRO, Calogero
;VETRO, Francesca
2016-01-01
Abstract
We prove the existence of a g-best proximity point for a pair of mappings, by using suitable hypotheses on a metric space. Moreover, we establish some convergence results for a variational inequality problem, by using the variational characterization of metric projections in a real Hilbert space. Our results are applicable to classical problems of optimization theory.
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