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Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

Muhammad Aqeel Ahmad Khan (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature....

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Paolamaria Pietramala (1991)

Commentationes Mathematicae Universitatis Carolinae

Let K be a closed convex subset of a Hilbert space H and T : K K a nonexpansive multivalued map with a unique fixed point z such that { z } = T ( z ) . It is shown that we can construct a sequence of approximating fixed points sets converging in the sense of Mosco to z .

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