Strong convergence of a system of generalized mixed equilibrium problem, split variational inclusion problem and fixed point problem in Banach spaces

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Authors

Abbas, Mujahid
Ibrahim, Yusuf
Khan, Abdul Rahim
De la Sen, Manuel

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MDPI

Abstract

The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result.

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Keywords

Split variational inclusion problem, Generalized mixed equilibrium problem, Fixed point problem, Maximal monotone operator, Left Bregman asymptotically nonexpansive mapping, Uniformly convex and uniformly smooth Banach space

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Citation

Abbas, M., Ibrahim, Y., Khan, A.R. et al 2019, 'Strong convergence of a system of generalized mixed equilibrium problem, split variational inclusion problem and fixed point problem in Banach spaces', Symmetry, vol. 11, no. 5, art. 722, pp. 1-21.