Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces
-
1863
Downloads
-
3039
Views
Authors
Sahar Mohamed Ali Abou Bakr
- Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt.
Abstract
This paper proves the existence of a unique common fixed point of two self mappings defined on complete cone quasi metric space \(\mathfrak{C}\) with respect to Banach algebra, consequently in particular, it proves the existence of only one fixed point of a generalized cyclic Banach algebra contraction and a cyclic Banach algebra Kannan type mappings with respect to a couple of non empty subsets \((A, B)\) of a complete cone quasi metric space \(\mathfrak{C}\). These existences extend the fixed point results of the attached references and then generalized the corresponding classical results in usual Banach spaces as well.
Share and Cite
ISRP Style
Sahar Mohamed Ali Abou Bakr, Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 10, 644--655
AMA Style
Abou Bakr Sahar Mohamed Ali, Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces. J. Nonlinear Sci. Appl. (2019); 12(10):644--655
Chicago/Turabian Style
Abou Bakr, Sahar Mohamed Ali. "Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces." Journal of Nonlinear Sciences and Applications, 12, no. 10 (2019): 644--655
Keywords
- Quasi metric spaces
- fixed point theorems
- \(\{a,b,c\}\) generalized contractions
- generalized \(\phi\) weak contractions
- cyclic contraction mappings
MSC
References
-
[1]
M. Abbas, V. Ćojbašić Rajić, T. Nazir, S. Radenović, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afr. Mat., 26 (2015), 17--30
-
[2]
S. M. Ali, Fixed point theorems of $\{a, b, c\}$ contraction and nonexpansive type mappings in weakly Cauchy normed spaces, Anal. Theory Appl., 29 (2013), 280--288
-
[3]
S. M. Ali Abou Bakr, Some Generalized Fixed Point Theorems of Contraction Type Mappings in Quasi Metric Spaces, J. Math. Stat., 14 (2017), 319--324
-
[4]
H. Aydi, E. Karapinar, B. Samet, Remarks on some recent fixed point theorems, Fixed Point Theory Appl., 2012 (2012), 6 pages
-
[5]
H. Çakally, A. Sönmez, Ç. Genç, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett., 25 (2012), 429--433
-
[6]
W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259--2261
-
[7]
P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages
-
[8]
E. El-Shobaky, S. M. Ali, M. S. Ali, Generalization of Banach contraction principle in two directions, J. Math. Stat., 3 (2007), 112--115
-
[9]
J. Fernandez, N. Malviya, S. Radenovič, K. Saxena, $F$--cone metric spaces over Banach algebra, Fixed Point Theory Appl., 2017 (2017), 18 pages
-
[10]
J. Fernandez, G. Modi, N. Malviya, Some fixed point theorems for contractive maps in N-cone metric spaces, Math. Sci. (Springer), 9 (2015), 33--38
-
[11]
J. Fernandez, K. Saxena, N. Malviya, Fixed points of expansive maps in partial cone metric spaces, Gazi University J. Sci., 27 (2014), 1085--1091
-
[12]
R. George, H. A. Nabwey, R. Rajagopalan, S. Radenovič, K. P. Reshma, Rectangular cone $b$--metric spaces over Banach algebra and contraction principle, Fixed Point Theory Appl., 2017 (2017), 15 pages
-
[13]
R. H. Haghi, S. Rezapour, N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799--1803
-
[14]
R. H. Haghi, S. Rezapour, N. Shahzad, Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450--454
-
[15]
H. P. Huang, S. Radenovič, Some fixed point results of generalised Lipschitz mappings on cone b-metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 566--583
-
[16]
L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorem of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468--1476
-
[17]
W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79--89
-
[18]
H. Liu, S. Y. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 2013 (2013), 10 pages
-
[19]
N. Malviya, B. Fisher, $N$--cone metric space and fixed points of asymptotically regular maps, Filomat, 2013 (2013), 11 pages
-
[20]
W. Rudin, Functional Analysis, McGraw-Hill, New York (1991)
-
[21]
N. Sharma, Fixed point theorem in cone $B$--metric spaces using contractive mappings, Global J. Pure Appl. Math., 13 (2017), 2997--3004