Convergence Theorems for Modified Mann Reich-Sabach Iteration Scheme for Approximating the Common Solution of Equilibrium Problems and Fixed Point Problems in Hilbert Spaces with Numerical Examples

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Felicia. O. Isiogugu*
P. Pillay
C. C. Okeke
F. U. Ogbuisi
P. U.Nwokoro

Abstract

Communication in Physical Sciences 2020, 5(4): 482-496


Received 25 May 2017/Revised 9 May 2018/Accepted 20 February 2020


It is proved that the modified Reich-Sabach iteration scheme introduced recently by Isiogugu et al. in a real Hilbert space , converges strongly to a common element of the fixed point sets of a finite family of multi-valued strictly pseudocontractive-type mappings and the set of solutions of a finite family of equilibrium problems. This work is a continuation of the study on the computability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of the sequences  and , from an arbitrary , where , , while  is the projection map and  is the sequence of the resolvent of the bifunction. The obtained results improve, complement and extend many results on equilibrium problems, multi-valued and single-valued mappings in the contemporary literature.

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Author Biographies

Felicia. O. Isiogugu*, University of Nigeria, Nsukka, Nigeria

Department of Mathematics

School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Westville Campus, Durban 4000, South Africa

P. Pillay, School of Mathematics, Statistics and Computer Sciences

School of Mathematics, Statistics and Computer Sciences,

C. C. Okeke, University of KwaZulu-Natal, Westville Campus, Durban 4000, South Africa

School of Mathematics, Statistics and Computer Sciences,

F. U. Ogbuisi, University of Nigeria, Nsukka, Nigeria

Department of Mathematics

P. U.Nwokoro, University of Nigeria, Nsukka, Nigeria

Department of Mathematics

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