TY - JOUR

T1 - An iterative algorithm for the system of split mixed equilibrium problem

AU - Karahan, Ibrahim

AU - Jolaoso, Lateef Olakunle

N1 - Funding Information:
L. O. Jolaoso is supported by the Postdoctoral research grant from the Sefako Makgatho Health Sciences University, South Africa. The authors thanks the reviewers for their valuable suggestions and comments which have improved the manuscript.
Publisher Copyright:
© 2020 Ibrahim Karahan and Lateef Olakunle Jolaoso, published by De Gruyter 2020.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - In this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

AB - In this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

KW - equilibrium problem

KW - fixed point

KW - nonexpansive mappings

KW - split problem

UR - http://www.scopus.com/inward/record.url?scp=85099293045&partnerID=8YFLogxK

U2 - 10.1515/dema-2020-0027

DO - 10.1515/dema-2020-0027

M3 - Article

AN - SCOPUS:85099293045

VL - 53

SP - 309

EP - 324

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

SN - 0420-1213

IS - 1

ER -