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Mathematics 2019, 7(3), 255; https://doi.org/10.3390/math7030255

Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems

1
and
2,3,*
1
College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
3
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
*
Author to whom correspondence should be addressed.
Received: 11 February 2019 / Accepted: 28 February 2019 / Published: 12 March 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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Abstract

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., López et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms. View Full-Text
Keywords: equilibrium problem; split variational inclusion problem; convex minimization problem; self-adaptive step size equilibrium problem; split variational inclusion problem; convex minimization problem; self-adaptive step size
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Tang, Y.; Cho, Y.J. Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems. Mathematics 2019, 7, 255.

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