The Existence and Approximation Fixed Point Theorems for Monotone Nonspreading Mappings in Ordered Banach Spaces

Authors

  • Khanitin Muangchoo-in Department of Exercise and Sports Science, Faculty of Sports and Health Science, 239, Moo. 4, Muang Chaiyaphum, Chaiyaphum 36000, Thailand; KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
  • Poom Kumam KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand; Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

DOI:

https://doi.org/10.26713/jims.v11i3-4.419

Keywords:

Ordered Banach space, Fixed point, Monotone nonspreading mapping, Mann iterative scheme

Abstract

In this paper, we proved some existence theorems of fixed points for monotone nonspreading mappings T in a Banach space E with the partial order ≤. In order to finding a fixed point of such a mapping T, moreover we proved the convergence theorem of Mann iterative schemes under the condition ∑n=1∞βn(1−βn)=∞, which contain βn=1n+1 as a special case.

Downloads

References

M. Bachar and M. A. Khamsi, Fixed points of monotone mappings and application to integral equations, Fixed Point Theory Appl. 2015 (2015), 110, DOI: 10.1186/s13663-015-0362-x.

B. A. B. Dehaish, M. A. Khamsi, Mann iteration process for monotone nonexpansive mappings, Fixed Point Theory Appl. 2015 (2015), 177, DOI: 10.1186/s13663-015-0416-0.

F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings relate to maximal monotone operators in Banach spaces, Arch. Math. (Basel) 91 (2008), 166 – 177, DOI: 10.1007/s00013-008-2545-8.

L. S. Liu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114 – 125, DOI: 10.1006/jmaa.1995.1289.

W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506 – 510, DOI: 10.1090/S0002-9939-1953-0054846-3.

E. Naraghirad, On an open question of Takasashi for nonpsreading mapping in Banach spaces, Fixed Point Theory Appl. 2013 (2013), 228, DOI: 10.1186/1687-1812-2013-228.

Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 591 – 597, DOI: 10.1090/S0002-9904-1967-11761-0.

W. Takahashi, Nonlinear Functional Analysis – Fixed Point Theory and its Applications, Yokohama Publishers Inc., Yokohama (2000).

H. K. Xu, Inequality in Banach spaces with applications, Nonlinear Anal. 16 (1991), 1127 – 1138, DOI: 10.1016/0362-546X(91)90200-K.

H. Zhang and Y. Su, Convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces, Nonlinear Anal. 71 (2009), 4572 – 4580, DOI: 10.1016/j.na.2009.03.033.

H. Zhou, Convergence theorems for ¸-strict pseudo-contractions in 2-uniformly smooth Banach spaces, Nonlinear Anal. 69 (2008), 3160 – 3173, DOI: 10.1016/j.na.2007.09.009.

Downloads

Published

2019-12-31
CITATION

How to Cite

Muangchoo-in, K., & Kumam, P. (2019). The Existence and Approximation Fixed Point Theorems for Monotone Nonspreading Mappings in Ordered Banach Spaces. Journal of Informatics and Mathematical Sciences, 11(3-4), 407–419. https://doi.org/10.26713/jims.v11i3-4.419

Issue

Vol. 11 No. 3-4 (2019)

Section

Research Article

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.