On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces
-
1529
Downloads
-
2879
Views
Authors
Stojan Huang
- School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China.
Ljiljana Paunović
- Teacher Education School in Prizren-Leposavić, Nemanjina b.b, 38218, Leposavic, Serbia.
Huaping Radenović
- Faculty of Mathematics and Information Technology, Dong Thap University, Dong Thap, Viêt Nam.
Abstract
In this paper we prove some new fixed point results in the context of ordered b-metric spaces for rational
Geraghty contractive mappings. Thus our results in the new context generalize, extend, unify, enrich and
complement fixed point theorems of contractive mappings in several aspects. One example is given to show
the validity of our results. In addition, we obtain the periodic property of these mappings.
Share and Cite
ISRP Style
Stojan Huang, Ljiljana Paunović, Huaping Radenović, On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 800--807
AMA Style
Huang Stojan, Paunović Ljiljana, Radenović Huaping, On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces. J. Nonlinear Sci. Appl. (2015); 8(5):800--807
Chicago/Turabian Style
Huang, Stojan, Paunović, Ljiljana, Radenović, Huaping. "On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 800--807
Keywords
- Fixed point
- b-metric space
- rational Geraghty contraction
- ordered b-metric space.
MSC
References
-
[1]
M. Abbas, V. Parvaneh, A. Razani, Periodic points of T-Ćirić generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19 (2012), 597–610.
-
[2]
A. G. B. Ahmad, Z. M. Fadail, M. Abbas, Z. Kadelburg, S. Radenović, Some fixed and periodic points in abstract metric spaces, Abstr. Appl. Anal., 2012 (2012), 15 pages.
-
[3]
A. Aghajani, M. Abbas, J. Roshan , Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), 941–960.
-
[4]
A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), 243–253.
-
[5]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133–181.
-
[6]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5–11.
-
[7]
D. Ðukić, Z. Kadelburg, S. Radenović, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal., 2011 (2011), 13 pages.
-
[8]
M. A. Geraghty, On contractive mappings, Proc. Am. Math. Soc., 40 (1973), 604–608.
-
[9]
N. Hussain, D. Ðorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 12 pages.
-
[10]
D. S. Jaggi , Some unique fixed point theorems, Indian J. Pure Appl. Math., 8 (1977), 223–230.
-
[11]
G. S. Jeong, B. E. Rhoades, Maps for which \(F (T) = F (T^n)\) , Fixed Point Theory Appl., 6 (2005), 71–131.
-
[12]
M. Jovanović, Z. Kadelburg, S. Radenović , Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010 (2010), 15 pages.
-
[13]
M. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., 2010 (2010), 7 pages.
-
[14]
H. K. Nashine, M. Imdad, M. Hasan, Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 42–50.
-
[15]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223–239.
-
[16]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin., Engl. Ser., 23 (2007), 2205–2212.
-
[17]
V. Parvaneh, J. Roshan, S. Radenović, Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations , Fixed Point Theory Appl., 2013 (2013), 19 pages.
-
[18]
A. C. M. Ran, M. C. B. Reurings, C. B. Martine, A fixed point theorem in partially ordered sets and some application to matrix equations , Proc. Am. Math. Soc., 132 (2004), 1435–1443.
-
[19]
J. R. Roshan, V. Parvaneh, N. Shobkolaei, S. Sedghi, W. Shatanawi , Common fixed points of almost generalized \((\psi,\varphi )_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages.
-
[20]
J. R. Roshan, V. Parvaneh, Z. Kadelburg , Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229–245.
-
[21]
R. J. Shahkoohi, A. Razani , Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, J. Inequal. Appl., 2014 (2014), 23 pages.