Fixed points for \(\alpha\)-admissible contractive mappings via simulation functions

Volume 9, Issue 10, pp 5544--5560 http://dx.doi.org/10.22436/jnsa.009.10.05

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)

• 2215 Downloads
• 3846 Views

Authors

Abdelbasset Felhi - Department of Mathematics and Statistics, College of Sciences, King Faisal University, Hafouf, P. O. Box 400 Post code. 31982, Saudi Arabia. Hassen Aydi - Department of Mathematics, College of Education of Jubail, University of Dammam, P. O.: 12020, Industrial Jubail 31961, Saudi Arabia. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan. Dong Zhang - School of Mathematical Sciences, Peking University, 100871, Beijing, China.

Abstract

Based on concepts of \(\alpha\)-admissible mappings and simulation functions, we establish some fixed point results in the setting of metric-like spaces. We show that many known results in the literature are simple consequences of our obtained results. We also provide some concrete examples to illustrate the obtained results.

Share and Cite

Keywords

• Metric-like
• fixed point
• simulation functions
• \(\alpha\)-admissible mappings.

MSC

•  47H10
•  54H25

References

• [1] T. Abdeljawad, E. Karapınar, K. Taş, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716--719


• [2] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages


• [3] H. Argoubi, B. Samet, C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (2015), 1082--1094


• [4] H. Aydi, A. Felhi, E. Karapınar, S. Sahmim, A Nadler-type fixed point theorem in metric-like spaces and applications, Miskolc Math. Notes, accepted (2015),


• [5] H. Aydi, A. Felhi, S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Math. Sci. (Springer), 9 (2015), 103--108


• [6] H. Aydi, M. Jellali, E. Karapınar, On fixed point results for \(\alpha\)-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21 (2016), 40--56


• [7] H. Aydi, E. Karapınar, Fixed point results for generalized \(\alpha-\psi\)-contractions in metric-like spaces and applications, Electron. J. Differential Equations, 2015 (2015), 15 pages


• [8] H. Aydi, E. Karapınar, C. Vetro, On Ekeland's variational principle in partial metric spaces, Appl. Math. Inf. Sci., 9 (2015), 257--262


• [9] R. George, R. Rajagopalan, S. Vinayagam, Cyclic contractions and fixed points in dislocated metric spaces, Int. J. Math. Anal., 7 (2013), 403--411


• [10] P. Hitzler, A. K. Seda, Dislocated topologies, J. Electr. Eng., 51 (2000), 3--7


• [11] E. Karapınar, P. Kumam, P. Salimi, On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 12 pages


• [12] F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189--1194


• [13] S. G. Matthews, Partial metric topology, Papers on general topology and applications, Flushing, NY, (1992), Ann. New York Acad. Sci., New York Acad. Sci., 1994 (1994), 183--197


• [14] B. Mohammadi, Sh. Rezapour, N. Shahzad, Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 10 pages


• [15] A. Nastasi, P. Vetro, Fixed point results on metric and partial metric spaces via simulation functions, J. Nonlinear Sci. Appl., 8 (2015), 1059--1069


• [16] S. J. O'Neill, Partial metrics, valuations, and domain theory, Papers on general topology and applications, Gorham, ME, (1995), 304-315, Ann. New York Acad. Sci., New York Acad. Sci., New York (1996)


• [17] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165