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Fixed Point Theorems for Iterated mappings via Caristi-Type Results

by Samih Lazaiz, Mohamed Aamri, Omar Zakary
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 156 - Number 4
Year of Publication: 2016
Authors: Samih Lazaiz, Mohamed Aamri, Omar Zakary
10.5120/ijca2016912419

Samih Lazaiz, Mohamed Aamri, Omar Zakary . Fixed Point Theorems for Iterated mappings via Caristi-Type Results. International Journal of Computer Applications. 156, 4 ( Dec 2016), 1-6. DOI=10.5120/ijca2016912419

@article{ 10.5120/ijca2016912419,
author = { Samih Lazaiz, Mohamed Aamri, Omar Zakary },
title = { Fixed Point Theorems for Iterated mappings via Caristi-Type Results },
journal = { International Journal of Computer Applications },
issue_date = { Dec 2016 },
volume = { 156 },
number = { 4 },
month = { Dec },
year = { 2016 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume156/number4/26694-2016912419/ },
doi = { 10.5120/ijca2016912419 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:01:39.448095+05:30
%A Samih Lazaiz
%A Mohamed Aamri
%A Omar Zakary
%T Fixed Point Theorems for Iterated mappings via Caristi-Type Results
%J International Journal of Computer Applications
%@ 0975-8887
%V 156
%N 4
%P 1-6
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we apply our former result [S. Lazaiz, K. Chaira, M. Aamri, and El M. Marhrani. Some remarks on Caristi type fixed point theorem. International Journal of Pure and Applied Mathematics, 104 (4): 585–597, 2015] to give a new results of iterated contraction mapping in complete metric space. As application we investigate the existence and uniqueness of solution for the nonlinear integral equation.

References
  1. Felix E Browder. On the convergence of successive approximations for nonlinear functional equations. In Indagationes Mathematicae (Proceedings), volume 71, pages 27–35. Elsevier, 1968.
  2. Ivar Ekeland. Sur les problemes variationnels. CR Acad. Sci. Paris Sér. AB, 275:A1057–A1059, 1972.
  3. H Brézis and FE Browder. A general principle on ordered sets in nonlinear functional analysis. Advances in Mathematics, 21(3):355–364, 1976.
  4. Jean-Pierre Aubin and Hélène Frankowska. Set-valued analysis. Springer Science & Business Media, 2009.
  5. Leila Gholizadeh. A fixed point theorem in generalized ordered metric spaces with application. J. Nonlinear Sci. Appl, 6:244–251, 2013.
  6. Adoon Pansuwan, Wutiphol Sintunavarat, Vahid Parvaneh, and Yeol Je Cho. Some fixed point theorems for (α , θ, k)- contractive multi-valued mappings with some applications. Fixed Point Theory and Applications, 2015(1):1–11, 2015.
  7. Stefan Banach. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math, 3(1):133–181, 1922.
  8. Ljubomir B Ciric. Generalized contractions and fixed-point theorems. Publ. Inst. Math.(Beograd)(NS), 12(26):19–26, 1971.
  9. Michael Edelstein. An extension of Banach’s contraction principle. Proceedings of the American Mathematical Society, 12(1):7–10, 1961.
  10. Yuqiang Feng and Sanyang Liu. Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings. Journal of Mathematical Analysis and Applications, 317(1):103–112, 2006.
  11. Jacek R Jachymski. Caristi’s fixed point theorem and selections of set-valued contractions. Journal of Mathematical Analysis and Applications, 227(1):55–67, 1998.
  12. Amram Meir and Emmett Keeler. A theorem on contraction mappings. Journal of Mathematical Analysis and Applications, 28(2):326–329, 1969.
  13. E Rakotch. A note on contractive mappings. Proceedings of the American Mathematical Society, 13(3):459–465, 1962.
  14. Ya I Alber and Sylvie Guerre-Delabriere. Principle of weakly contractive maps in hilbert spaces. In New Results in Operator Theory and Its Applications, pages 7–22. Springer, 1997.
  15. BE Rhoades. Some theorems on weakly contractive maps. Nonlinear Analysis: Theory, Methods & Applications, 47(4):2683–2693, 2001.
  16. PN Dutta and Binayak S Choudhury. A generalisation of contraction principle in metric spaces. Fixed Point Theory and Applications, 2008(1):1–8, 2008.
  17. VM Sehgal. A fixed point theorem for mappings with a contractive iterate. Proceedings of the American Mathematical Society, 23(3):631–634, 1969.
  18. VW Bryant. A remark on a fixed-point theorem for iterated mappings. The American Mathematical Monthly, 75(4):399– 400, 1968.
  19. LF Guseman. Fixed point theorems for mappings with a contractive iterate at a point. Proceedings of the American Mathematical Society, 26(4):615–618, 1970.
  20. James Caristi. Fixed point theorems for mappings satisfying inwardness conditions. Transactions of the American Mathematical Society, 215:241–251, 1976.
  21. S Lazaiz, K Chaira, M Aamri, and El M Marhrani. Some remarks on Caristi type fixed point theorem. International Journal of Pure and Applied Mathematics, 104(4):585–597, 2015.
  22. Michael A Geraghty. On contractive mappings. Proceedings of the American Mathematical Society, 40(2):604–608, 1973.
Index Terms

Computer Science
Information Sciences

Keywords

Fixed point Caristi’s theorem Remarks Nonlinear Integral equations

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