Fixed point theorems for (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings on \(\alpha-\eta\)-complete partial metric spaces
-
1838
Downloads
-
2696
Views
Authors
Ali Farajzadeh
- Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149, Iran.
Preeyaluk Chuadchawna
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
Anchalee Kaewcharoen
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
Abstract
In this paper, the notion of strictly (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings is introduced where
the continuity of \(\xi\) is relaxed. The existence of fixed point theorems for such mappings in the setting of
\(\alpha,\eta\)-complete partial metric spaces are provided. The results of the paper can be viewed as the extension
of the recent results obtained in the literature. Furthermore, we assure the fixed point theorems in partial
complete metric spaces endowed with an arbitrary binary relation and with a graph using our obtained
results.
Share and Cite
ISRP Style
Ali Farajzadeh, Preeyaluk Chuadchawna, Anchalee Kaewcharoen, Fixed point theorems for (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings on \(\alpha-\eta\)-complete partial metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 1977--1990
AMA Style
Farajzadeh Ali, Chuadchawna Preeyaluk, Kaewcharoen Anchalee, Fixed point theorems for (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings on \(\alpha-\eta\)-complete partial metric spaces. J. Nonlinear Sci. Appl. (2016); 9(5):1977--1990
Chicago/Turabian Style
Farajzadeh, Ali, Chuadchawna, Preeyaluk, Kaewcharoen, Anchalee. "Fixed point theorems for (\(\alpha,\eta,\psi,\xi\))-contractive multi-valued mappings on \(\alpha-\eta\)-complete partial metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 1977--1990
Keywords
- \(\alpha،\eta\)-complete partial metric spaces
- \(\alpha،\eta\)-continuity
- (\(\alpha،\eta،\psi،\xi\))-contractive multi-valued mappings
- \(\alpha\)-admissible multi-valued mappings with respect to \(\eta\).
MSC
References
-
[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric space, J. Math. Anal. Appl., 341 (2008), 416-420.
-
[2]
M. U. Ali, T. Kamran, E. Karapinar , (\(\alpha,\psi,\xi\))-Contractive multi-valued mappings, Fixed point theory Appl., 2014 (2014), 8 pages.
-
[3]
I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud., 1 (2008), 1-8.
-
[4]
I. Altun, F. Sola, H. Simsek, Generalized contraction on partial metric spaces, Topology Appl., 157 (2010), 2778-2785.
-
[5]
P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized \(\alpha-\psi\)-contractions, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., 108 (2014), 519-526.
-
[6]
H. Aydi , Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4 (2011), 210-217.
-
[7]
H. Aydi, Common fixed point for four maps in ordered partial metric spaces, Fasc. Math., 49 (2012), 15-31.
-
[8]
H. Aydi, M. Abbas, C. Vetro , Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces , Topology Appl., 159 (2012), 3234-3242.
-
[9]
R. M. Bianchini, M. Grandolfi , Transformazioni tipo contravtivo generalizzato in uno spazio metrico, Atti Accad. Naz. Lincei, Rend. Ci. Sci. Fis. Mat. Nat., 45 (1968), 212-216.
-
[10]
N. Hussain, M. A. Kutbi, P. Salimi , Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 11 pages.
-
[11]
M. A. Kutbi, W. Sintunavrat, On new fixed pont results for (\(\alpha,\psi,\xi\))-contractive multi-valued mappings on \(\alpha\)- complete metric spaces and their consequences, Fixed point theory Appl., 2015 (2015), 15 pages.
-
[12]
S. G. Matthews, Partial metric topology, Papers on general topology and applications, Ann. New York Acad. Sci., (1994), 183-197.
-
[13]
B. Mohammadi, S. Rezapour, S. Naseer , Some results on fixed points of \(\alpha-\psi\)-Ciric generalized multifunction, Fixed point theory Appl., 2013 (2013), 10 pages.
-
[14]
S. B. J. Nadler , Multi-valued contraction mappings , Pacific J. Math., 30 (1969), 475-488.
-
[15]
P. D. Proinov, A generalization of the Banach contraction principle with high order of convergence of successive approximations, Nonlinear Anal., 67 (2007), 2361-2369.
-
[16]
B. Samet, C. Vetro, P. Vetro, Fixed-point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.
-
[17]
W. Sintunavarat, P. Kumam , Weak condition for generalized multi-valued \((f, alpha,\beta)\)-weak contraction mappings, Appl. Math. Lett., 24 (2011), 460-465.