Open AccessStrong convergence of a selection of ishikawa-reich-sabach-type algorithm
Author(s) -
Obiageli Isiogugu Felicia,
Paranjothi Pillay,
Osuo-Siseken Uzoma-Oguguo
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1906505i
Subject(s) - mathematics , sequence (biology) , computability , convergence (economics) , regular polygon , hilbert space , type (biology) , algorithm , selection (genetic algorithm) , metric space , combinatorics , discrete mathematics , pure mathematics , computer science , artificial intelligence , biology , economic growth , genetics , geometry , ecology , economics
We establish the strong convergence of a selection of an Ishikawa-Reich-Sabach iteration scheme for approximating the common elements of the set of fixed points F(T) of a multi-valued (or singlevalued) pseudocontractive-type mapping T and the set of solutions EP(F) of an equilibrium problem for a bifunction F in a real Hilbert space H. This work is a contribution to the study on the computability and applicability of algorithms for approximating the solutions of equilibrium problems for bifunctions involving the construction of the sequence {Kn}?n=1 of closed convex subsets of H from an arbitrary x0 ? H and the sequence {xn}?n=1 of the metric projections of x0 into Kn. The results obtained are contributions to the resolution of the controversy over the computability and applicability of such algorithms in the contemporary literature.