Geodesic
A modified Krasnoselskii-Mann algorithm for equilibrium and fixed point problems for nonexpansive mappings in Hilbert spaces
Novi Sad Journal of Mathematics, Tome 51 (2021) no. 1.

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In this paper, we introduce two iterative shemes (one implicit and one explicit) by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of nonexpansive mappings in Hilbert spaces. We prove that both approaches converge strongly to a common element of the set of the equilibrium points and the set of fixed points of nonexpansive mappings. Such common element is the unique solution of a variational inequality, which is the minimum-norm element of the above two sets. Applications to split feasibility problem and optimization problem are given. Finally, numerical example is given to demonstrate the implementability of our algorithm.
Publié le :
DOI : 10.30755/NSJOM.08480
Classification : 47H05, 47H10, 47J20
Keywords: Krasnoselskii-Mann algorithm, Strong convergence, Fixed point problems, Equilibrium problems, Nonexpansive mappings 
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     author = {Thierno M.M. Sow},
     title = {A modified {Krasnoselskii-Mann} algorithm   
	for equilibrium and fixed point problems for  nonexpansive mappings in {Hilbert} spaces},
     journal = {Novi Sad Journal of Mathematics},
     pages = {13 - 26},
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     volume = {51},
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     year = {2021},
     doi = {10.30755/NSJOM.08480},
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Thierno M.M. Sow. A modified Krasnoselskii-Mann algorithm   
	for equilibrium and fixed point problems for  nonexpansive mappings in Hilbert spaces. Novi Sad Journal of Mathematics, Tome 51 (2021) no. 1. doi : 10.30755/NSJOM.08480. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.08480/

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