Next Article in Journal
Chen’s Biharmonic Conjecture and Submanifolds with Parallel Normalized Mean Curvature Vector
Next Article in Special Issue
A New Optimal Family of Schröder’s Method for Multiple Zeros
Previous Article in Journal
Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions
Previous Article in Special Issue
A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems
Article

Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings

1
KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
2
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
3
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
4
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
5
Rajamangala University of Technology Phra Nakhon, 399 Samsen Rd., Vachira Phayaban, Dusit, Bangkok 10300, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 709; https://doi.org/10.3390/math7080709
Received: 9 July 2019 / Revised: 24 July 2019 / Accepted: 26 July 2019 / Published: 6 August 2019
(This article belongs to the Special Issue Computational Methods in Analysis and Applications)
In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern’s algorithm. View Full-Text
Keywords: fixed point; Bregman distance; Bregman function; Bregman–Opial property; generalized α-nonexpansive mapping fixed point; Bregman distance; Bregman function; Bregman–Opial property; generalized α-nonexpansive mapping
Show Figures

Figure 1

MDPI and ACS Style

Muangchoo, K.; Kumam, P.; Cho, Y.J.; Dhompongsa, S.; Ekvittayaniphon, S. Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings. Mathematics 2019, 7, 709. https://doi.org/10.3390/math7080709

AMA Style

Muangchoo K, Kumam P, Cho YJ, Dhompongsa S, Ekvittayaniphon S. Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings. Mathematics. 2019; 7(8):709. https://doi.org/10.3390/math7080709

Chicago/Turabian Style

Muangchoo, Kanikar, Poom Kumam, Yeol J. Cho, Sompong Dhompongsa, and Sakulbuth Ekvittayaniphon. 2019. "Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings" Mathematics 7, no. 8: 709. https://doi.org/10.3390/math7080709

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

Article Access Map by Country/Region

1
Back to TopTop