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Mathematics 2019, 7(2), 167; https://doi.org/10.3390/math7020167

Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings

School of Science, University of Phayao, Phayao 56000, Thailand
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Received: 18 December 2018 / Revised: 4 February 2019 / Accepted: 7 February 2019 / Published: 13 February 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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Abstract

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem. View Full-Text
Keywords: strong convergence; weak convergence; fixed point; nonexpansive mappings; maximal monotone operator; inverse strongly monotone mapping; hilbert space strong convergence; weak convergence; fixed point; nonexpansive mappings; maximal monotone operator; inverse strongly monotone mapping; hilbert space
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Cholamjiak, P.; Kesornprom, S.; Pholasa, N. Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings. Mathematics 2019, 7, 167.

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