A generalized nonlinear iterative algorithm for the explicit midpoint rule of nonexpansive semigroup

Abstract

In this paper, we introduce a new iterative midpoint rule for finding a solution of xed point problem for a nonexpansive semigroup in real Hilbert spaces. We establish a strong convergence theorem for the sequences generated by our proposed iterative scheme. Furthermore, we provide application to Fredholm integral equations. A
numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.

Keywords

• Nonexpansive semigroup,equilibrium problem,midpoint method,strongly positive linear bounded operator

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