Fixed point theorems for \(\Theta\)-contractions in left \(K\)-complete \(T_{1}\)-quasi metric space
-
1501
Downloads
-
2550
Views
Authors
Durdana Lateef
- Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara, 41411, Kingdom of Saudi Arabia.
Jamshaid Ahmad
- Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia.
Abstract
The aim of this paper is to define \(\Theta
_{\beta }^{u}=\left \{ v\in \mathcal{J}u:\Theta (\varrho (u,v))\leq \lbrack
\Theta (\varrho (u,\mathcal{J}u))]^{\beta }\right \} \) and establish some
new fixed point theorems in the setting of left \(K\)-complete \(T_{1}\)-quasi
metric space. Our theorems generalize, extend, and unify several results of
literature.
Share and Cite
ISRP Style
Durdana Lateef, Jamshaid Ahmad, Fixed point theorems for \(\Theta\)-contractions in left \(K\)-complete \(T_{1}\)-quasi metric space, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 10, 667--674
AMA Style
Lateef Durdana, Ahmad Jamshaid, Fixed point theorems for \(\Theta\)-contractions in left \(K\)-complete \(T_{1}\)-quasi metric space. J. Nonlinear Sci. Appl. (2019); 12(10):667--674
Chicago/Turabian Style
Lateef, Durdana, Ahmad, Jamshaid. "Fixed point theorems for \(\Theta\)-contractions in left \(K\)-complete \(T_{1}\)-quasi metric space." Journal of Nonlinear Sciences and Applications, 12, no. 10 (2019): 667--674
Keywords
- \(\Theta\)-contractions
- property \(P\)
- property \(Q\)
- fixed points
MSC
References
-
[1]
M. Abbas, B. Ali, S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl., 2013 (2013), 11 pages
-
[2]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized $F$-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 18 pages
-
[3]
A. Al-Rawashdeh, J. Ahmad, Common Fixed Point Theorems for JS-Contractions, Bull. Math. Anal. Appl., 8 (2016), 12--22
-
[4]
I. Altun, B. Damjanović, D. Djorić, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23 (2010), 310--316
-
[5]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133--181
-
[6]
I. Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory Appl., 2006 (2006), 7 pages
-
[7]
H. Dağ, G. Minak, I. Altun, Some fixed point results for multivalued $F$--contractions on quasi metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 111 (2017), 177--187
-
[8]
H. A. Hançer, G. Minak, I. Altun, On a broad category of multivalued weakly Picard operators, Fixed Point Theory, 18 (2017), 229--236
-
[9]
N. Hussain, J. Ahmad, L. Ćirić, A. Azam, Coincidence point theorems for generalized contractions with application to integral equations, Fixed Point Theory Appl., 2015 (2015), 13 pages
-
[10]
N. Hussain, V. Parvaneh, B. Samet, C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 17 pages
-
[11]
G. S. Jeong, B. E. Rhoades, Maps for which $F(T)=F(T^{n})$, In: Fixed Point Theory and Applications, Nova Science Publishers, 2007 (2007), 71--105
-
[12]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages
-
[13]
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261--263
-
[14]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771--779
-
[15]
B. Samet, C. Vetro, P. Vetro, Fixed point theorem for $\alpha -\psi $ contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165
-
[16]
F. Vetro, A generalization of Nadler fixed point theorem, Carpathian J. Math., 31 (2015), 403--410