Pair \((F,h)\) upper class and \((\alpha ,\mu)\)-generalized multivalued rational type contractions
-
2628
Downloads
-
4939
Views
Authors
Nantaporn Chuensupantharat
- KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
Poom Kumam
- KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
- KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science (TaCS) Center, Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan.
Arslan Hojat Ansari
- Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Muhammad Usman Ali
- School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, H-12, Islamabad, Pakistan.
Abstract
In this paper, we introduce notions of \((\alpha ,\mu)\)-generalized rational contraction conditions and investigate the existence of the
fixed point of such mappings on complete metric spaces. To illustrate our result we also construct an example.
Share and Cite
ISRP Style
Nantaporn Chuensupantharat, Poom Kumam, Arslan Hojat Ansari, Muhammad Usman Ali, Pair \((F,h)\) upper class and \((\alpha ,\mu)\)-generalized multivalued rational type contractions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 2868--2878
AMA Style
Chuensupantharat Nantaporn, Kumam Poom, Ansari Arslan Hojat, Ali Muhammad Usman, Pair \((F,h)\) upper class and \((\alpha ,\mu)\)-generalized multivalued rational type contractions. J. Nonlinear Sci. Appl. (2017); 10(6):2868--2878
Chicago/Turabian Style
Chuensupantharat, Nantaporn, Kumam, Poom, Ansari, Arslan Hojat, Ali, Muhammad Usman. "Pair \((F,h)\) upper class and \((\alpha ,\mu)\)-generalized multivalued rational type contractions." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 2868--2878
Keywords
- \(\alpha\)-admissible
- \(\mu\)-subadmissible
- fixed point
- \((\alpha ،\mu)\)-generalized multivalued rational contraction
- pair \((F، h)\) upper class condition.
MSC
References
-
[1]
M. U. Ali, T. Kamran, On (\(\alpha^*,\psi\) )-contractive multi-valued mappings, Fixed Point Theory Appl., 2013 (2013), 7 pages.
-
[2]
M. U. Ali, T. Kamran, E. Karapınar, A new approach to (\(\alpha,\psi\) )-contractive nonself multivalued mappings, J. Inequal. Appl., 2014 (2014), 9 pages.
-
[3]
M. U. Ali, T. Kamran, E. Karapınar, (\(\alpha,\psi,\xi\))-contractive multivalued mappings, Fixed Point Theory Appl., 2014 (2014), 8 pages.
-
[4]
M. U. Ali, T. Kamran, W. Sintunavarat, P. Katchang, Mizoguchi-Takahashi’s fixed point theorem with \(\alpha,\eta\) functions, Abstr. Appl. Anal., 2013 (2013), 4 pages.
-
[5]
P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized \(\alpha-\psi\)-contractions, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 108 (2014), 519–526.
-
[6]
A. H. Ansari, Note on ”\(\alpha\)-admissible mappings and related fixed point theorems”, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, September , (2014), 373–376.
-
[7]
A. H. Ansari, S. Shukla, Some fixed point theorems for ordered F-(F, h)-contraction and subcontraction in 0-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), 37–53.
-
[8]
J. H. Asl, S. Rezapour, N. Shahzad, On fixed points of \(\alpha-\psi\)-contractive multifunctions, Fixed Point Theory Appl., 2012 (2012), 6 pages.
-
[9]
N. Hussain, P. Salimi, A. Latif, Fixed point results for single and set-valued \(\alpha-\eta-\psi\)-contractive mappings, Fixed Point Theory Appl., 2013 (2013), 23 pages.
-
[10]
T. Kamran, Mizoguchi-Takahashi’s type fixed point theorem, Comput. Math. Appl., 57 (2009), 507–511.
-
[11]
E. Karapınar, R. Ali, T. Kamran, M. U. Ali, Generalized multivalued rational type contractions, , 9 (2016), 26–36.
-
[12]
E. Karapınar, B. Samet, Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 17 pages.
-
[13]
Q. Kiran, M. U. Ali, T. Kamran, Generalization of Mizoguchi-Takahashi type contraction and related fixed point theorems, J. Inequal. Appl., 2014 (2014), 9 pages.
-
[14]
G. Mınak, I. Altun, Some new generalizations of Mizoguchi-Takahashi type fixed point theorem, J. Inequal. Appl., 2013 (2013), 10 pages.
-
[15]
B. Mohammadi, S. Rezapour, On modified \(\alpha-\phi\)-contractions, J. Adv. Math. Stud., 6 (2013), 162–166.
-
[16]
B. Mohammadi, S. Rezapour, N. Shahzad, Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 10 pages.
-
[17]
S. Rezapour, M. E. Samei, Some fixed point results for \(\alpha-\psi\)-contractive type mappings on intuitionistic fuzzy metric spaces, J. Adv. Math. Stud., 7 (2014), 176–181.
-
[18]
P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 19 pages.
-
[19]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165.