Next Article in Journal
The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds
Next Article in Special Issue
Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings
Previous Article in Journal
A Subclass of Bi-Univalent Functions Based on the Faber Polynomial Expansions and the Fibonacci Numbers
Previous Article in Special Issue
Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Mathematics 2019, 7(2), 161; https://doi.org/10.3390/math7020161

Convergence Theorems for Generalized Viscosity Explicit Methods for Nonexpansive Mappings in Banach Spaces and Some Applications

1
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand
2
KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
3
KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
4
Renewable Energy Research Centre & Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
5
School of Science, University of Phayao, Phayao 56000, Thailand
*
Authors to whom correspondence should be addressed.
Received: 17 December 2018 / Revised: 2 February 2019 / Accepted: 3 February 2019 / Published: 11 February 2019
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
Full-Text   |   PDF [837 KB, uploaded 11 February 2019]   |  

Abstract

In this paper, we introduce a generalized viscosity explicit method (GVEM) for nonexpansive mappings in the setting of Banach spaces and, under some new techniques and mild assumptions on the control conditions, prove some strong convergence theorems for the proposed method, which converge to a fixed point of the given mapping and a solution of the variational inequality. As applications, we apply our main results to show the existence of fixed points of strict pseudo-contractions and periodic solutions of nonlinear evolution equations and Fredholm integral equations. Finally, we give some numerical examples to illustrate the efficiency and implementation of our method. View Full-Text
Keywords: nonexpansive mapping; Banach space; strong convergence; viscosity iterative method; nonlinear evolution equation; Fredholm integral equation nonexpansive mapping; Banach space; strong convergence; viscosity iterative method; nonlinear evolution equation; Fredholm integral equation
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Sunthrayuth, P.; Pakkaranang, N.; Kumam, P.; Thounthong, P.; Cholamjiak, P. Convergence Theorems for Generalized Viscosity Explicit Methods for Nonexpansive Mappings in Banach Spaces and Some Applications. Mathematics 2019, 7, 161.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top