Strong convergence of split equality variational inequality and fixed point problem
Received: 16 June 2016
Accepted in revised form: 4 November 2016
Mathematics Subject Classification (2010): 47J25, 47N10, 65J15, 90C25.
Keywords: Split equality problem, fixed point, quasi-nonexpansive mapping, variational inequality.
[a]:University of Science and Technology of Mazandaran, Department of Mathematics, Box: 48518-78195, Behshahr, Iran and Institute for Research in Fundamental Science, School of Mathematics, (IPM) P.O.Box:19395-5746, Tehran, Iran
Abstract: The main purpose of this paper is to introduce a new algorithm for finding a solution of split equality variational inequality problem for monotone and Lipschitz continuous operators and common fixed points of a finite family of quasi-nonexpansive mappings in the setting of infinite dimensional Hilbert spaces. Under suitable conditions, we prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the split equality variational inequality and fixed point problem in Hilbert spaces. Our results improve and generalize some recent results in the literature.
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