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H.K. Xu: Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298(2004) 279-291

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Article

The Viscosity Iterative Algorithms for the Implicit Double Midpoint Rule of Nonexpansive Mappings in Hilbert Spaces

1University of the Gambia, Brikama Campus, Gambia


American Journal of Mathematical Analysis. 2020, Vol. 8 No. 1, 1-8
DOI: 10.12691/ajma-8-1-1
Copyright © 2020 Science and Education Publishing

Cite this paper:
John T Mendy. The Viscosity Iterative Algorithms for the Implicit Double Midpoint Rule of Nonexpansive Mappings in Hilbert Spaces. American Journal of Mathematical Analysis. 2020; 8(1):1-8. doi: 10.12691/ajma-8-1-1.

Correspondence to: John  T Mendy, University of the Gambia, Brikama Campus, Gambia. Email: jt.mendy@utg.edu.gm

Abstract

In this paper, we study the viscosity iterative algorithms for the implicit double midpoint rule in real Hilbert space and prove strong convergence of the sequence {un} to a fixed point of T. As an application we employ our method to obtain an application of it in convex minimization and the solution of Fredholm type of integral equations.

Keywords