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

Abstract


In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudo-contractions 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.

Keywords


fixed point; strict pseudo-contraction; equilibrium problem; variational inequality problem; inverse strongly monotone mapping; shrinking projection method

Mathematics Subject Classification (2010)


Primary 47H05, 47H09; Secondary 49H05

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