Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problems in \(M\)-metric spaces

Volume 9, Issue 6, pp 4489--4499 http://dx.doi.org/10.22436/jnsa.009.06.87

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1554 Downloads
• 2757 Views

Authors

Adoon Pansuwan - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand. Wutiphol Sintunavarat - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand. Jae Young Choi - Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Korea. Yeol Je Cho - Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Korea. - Center for General Education, China Medical University, Taichung 40402, Taiwan.

Abstract

In this paper, we introduce several types of Ulam-Hyers stability, well-posedness and limit shadowing property of the fixed point problem in \(M\)-metric spaces. Also, we give such results for fixed point problems of Banach and Kannan contractive mappings in \(M\)-metric spaces and provide two examples to illustrate the results presented herein.

Share and Cite

Keywords

• Fixed point
• limit shadowing property
• M-metric space
• Ulam-Hyers stability
• well-posedness.

MSC

•  47H09
•  47H10
•  54H25

References

• [1] K. Abodayeh, N. Mlaiki, T. Abedljawad, W. Shatanawi , Relations between partial metrics and M-metrics, Caristi- Kirk's theorem in M-metric type spaces, J. Math. Anal., ( to appear),


• [2] M. Asadi, Fixed point theorems for Meir-Keeler type mappings in M-metric spaces with applications, Fixed Point Theory Appl., 2015 (2015), 10 pages.


• [3] M. Asadi, E. Karapinar, P. Salimi , New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014), 9 pages.


• [4] A. Azam, F. Brian, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), 243-253.


• [5] S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math. , 3 (1922), 133-181.


• [6] M. F. Bota, E. Karapinar, O. Mlesnite, Ulam-Hyers stability results for fixed point problems via \(\alpha-\psi\) -contractive mapping in (b)-metric space, Abstr. Appl. Anal., 2013 (2013), 6 pages.


• [7] M. F. Bota-Boriceanu, A. Petrusel, Ulam-Hyers stability for operatorial equations, An. Stiint. Univ. Al. I. Cuza Iasi. Mat., 57 (2011), 65-74.


• [8] S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727-730.


• [9] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.


• [10] F. S. De Blassi, J. Myjak, Sur la porosite des contractions sans point fixe, (French) [On the porosity of the set of contractions without fixed points], C. R. Acad. Sci. Paris Sr. I Math., 308 (1989), 51-54.


• [11] R. Kannan, Some results on fixed points II, Amer. Math. Monthly, 76 (1969), 405-408.


• [12] B. K. Lahiri, P. Das, Well-posedness and porosity of certain classes of operators, Demonstratio Math., 38 (2005), 169-176.


• [13] Z. Ma, L. Jiang, H. Sun, C*-algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory Appl., 2014 (2014), 11 pages.


• [14] S. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci., 728 (1994), 183-197.


• [15] S. Reich, A. J. Zaslavski, Well-posedness of fixed point problems, Far East J. Math. Sci., 3 (2001), 393-401.