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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Date
Authors
Abbas, Mujahid
Ibrahim, Yusuf
Khan, Abdul Rahim
De la Sen, Manuel
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
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.