Some common fixed point results of graphs on \(b\)-metric space
-
1607
Downloads
-
2528
Views
Authors
Zead Mustafa
- Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar.
M. M. M. Jaradat
- Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar.
H. M. Jaradat
- Department of Mathematics, Al al-Bayt University, Jordan.
- Department of Mathematics and Applied Sciences, Dhofar University, Salalah, Oman.
Abstract
The aim of this paper is to present some coincidence point results and common fixed points for pair
of self-mappings satisfying generalized contractive condition in the framework of b-metric spaces endowed
with a graph. We present applications and some examples to illustrate the main result.
Share and Cite
ISRP Style
Zead Mustafa, M. M. M. Jaradat, H. M. Jaradat, Some common fixed point results of graphs on \(b\)-metric space, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4838--4851
AMA Style
Mustafa Zead, Jaradat M. M. M., Jaradat H. M., Some common fixed point results of graphs on \(b\)-metric space. J. Nonlinear Sci. Appl. (2016); 9(6):4838--4851
Chicago/Turabian Style
Mustafa, Zead, Jaradat, M. M. M., Jaradat, H. M.. "Some common fixed point results of graphs on \(b\)-metric space." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4838--4851
Keywords
- Coincidence point
- common fixed point with graph
- b-metric Space.
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]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), 941--960
-
[3]
S. Aleomraninejad, S. Rezapour, N. Shahzad, Fixed point results on subgraphs of directed graphs, Math. Sci., 7 (2013), 1--3
-
[4]
M. R. Alfuraidan, M. A. Khamsi, Caristi fixed point theorem in metric spaces with a graph, Abstr. Appl. Anal., 2014 (2014), 5 pages
-
[5]
I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, (Russian), Funct. Anal. Gos. Ped. Inst. Unianowsk, 30 (1989), 26--37
-
[6]
I. Beg, A. R. Butt, S. Radojević, The contraction principle for set valued mappings on a metric space with a graph, Comput. Math. Appl., 60 (2010), 1214--1219
-
[7]
F. Bojor, Fixed point of \(\phi\)-contraction in metric spaces endowed with a graph, An. Univ. Craiova Ser. Mat. Inform., 37 (2010), 85--92
-
[8]
F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. Ştiinţ. Univ. Ovidius Constantá Ser. Mat., 20 (2012), 31--40
-
[9]
J. A. Bondy, U. S. R. Murty, Graph theory with applications, American Elsevier Publishing Co., Inc., New York (1976)
-
[10]
M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Stud. Univ. Babes-Bolyai Math., 54 (2009), 3--14
-
[11]
M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4 (2009), 285--301
-
[12]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5--11
-
[13]
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263--276
-
[14]
F. Echenique, A short and constructive proof of Tarski's fixed-point theorem, Internat. J. Game Theory, 33 (2005), 215--218
-
[15]
R. Espínola, W. A. Kirk, Fixed point theorems in R-trees with applications to graph theory, Topology Appl., 153 (2006), 1046--1055
-
[16]
J. L. Gross, J. Yellen, Graph theory and its applications, Discrete Math. Appl., Boca Raton (2006)
-
[17]
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly (\(\psi,\varphi, L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory and Appl., 2013 (2013), 18 pages
-
[18]
N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677--1684
-
[19]
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359--1373
-
[20]
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261--263
-
[21]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771--779
-
[22]
G. Jungck, Common fixed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc., 103 (1988), 977--983
-
[23]
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4 (1996), 199--215
-
[24]
G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl., 325 (2007), 1003--1012
-
[25]
M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123--3129
-
[26]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 26 pages
-
[27]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed point theorems for weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces, J. Inequal. Appl., 2014 (2014), 14 pages
-
[28]
M. Păcurar, Sequences of almost contractions and fixed points in b-metric spaces, An. Univ. Vest Timis. Ser. Mat.-Inform., 48 (2010), 125--137
-
[29]
R. P. Pant, Common fixed points of noncommuting mappings, Math. Anal. Appl., 188 (1994), 436--440
-
[30]
S. Sedghi, N. Shobkolaei, J. R. Roshan, W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik, 66 (2014), 190--201
-
[31]
S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.), 32 (1982), 149--153
-
[32]
S. L. Singh, B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl., 55 (2008), 2512--2520