Solution of a class of equilibrium problems and variational inequalities in FC spaces

Gayatri Pany (), Ram N. Mohapatra () and Sabyasachi Pani ()
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Gayatri Pany: IIT
Ram N. Mohapatra: University of Central Florida
Sabyasachi Pani: IIT

Annals of Operations Research, 2018, vol. 269, issue 1, No 27, 565-582

Abstract: Abstract In this paper, we study a class of mixed variational-like inequalities with respect to generalized weakly relaxed $$\eta {-}\alpha $$ η - α monotone mappings, involving nonlinear bifunctions, in finitely continuous topological space, in short FC space. Existence of the solution to the problem is established relaxing convexity and linearity condition by using generalized RKKM theorem. We have proposed a proximal iterative scheme using auxiliary principle technique. Solvability of the auxiliary variational inequality problem is established. Finally convergence of the iterates to the exact solution is proved. Some results with application to equilibrium problem are also discussed.

Keywords: Mixed variational-like inequality; Generalized weakly relaxed $$\eta {-}\alpha $$ η - α monotonicity; FC space; Proximal iterative scheme; Auxiliary principle technique (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10479-017-2506-3

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