New Geraghty type contractions on metric-like spaces
- Department of Mathematics, College of Education of Jubail, University of Dammam, P. O. 12020, Industrial Jubail 31961, Saudi Arabia.
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
- Department of Mathematics and Statistics, College of Sciences, King Faisal University, Hafouf, Saudi Arabia.
- Faculty of Basic Science, University of Bonab, Bonab, Iran.
Very recently, Fulga and Proca [A. Fulga, A. M. Proca, Abstr. Appl. Anal., (In press)] considered new Geraghty type
contraction mappings and established a fixed point theorem for such mappings in complete metric spaces. In this paper, we
prove the analogous result in the class of metric-like spaces which generalizes the main result of Karapinar et al. [E. Karapınar, H.
H. Alsulami, M. Noorwali, Fixed Point Theory Appl., 2015 (2015), 22 pages]. We give some examples illustrating the presented
result where [E. Karapınar, H. H. Alsulami, M. Noorwali, Fixed Point Theory Appl., 2015 (2015), 22 pages] is not applicable. An
application is also provided.
Share and Cite
Hassen Aydi, Abdelbasset Felhi, Hojjat Afshari, New Geraghty type contractions on metric-like spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 780--788
Aydi Hassen, Felhi Abdelbasset, Afshari Hojjat, New Geraghty type contractions on metric-like spaces. J. Nonlinear Sci. Appl. (2017); 10(2):780--788
Aydi, Hassen, Felhi, Abdelbasset, Afshari, Hojjat. "New Geraghty type contractions on metric-like spaces." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 780--788
- Fixed point
- Geraghty type contraction
- metric-like space.
C. T. Aage, J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci. (Ruse), 59 (2008), 2941–2948.
S. A. Al-Mezel, C.-M. Chen, E. Karapınar, V. Rakočević, Fixed point results for various \(\alpha\)-admissible contractive mappings on metric-like spaces, Abstr. Appl. Anal., 2014 (2014 ), 15 pages.
H. H. Alsulami, E. Karapınar, H. Piri, Fixed points of modified F-contractive mappings in complete metric-like spaces, J. Funct. Spaces, 2015 (2015 ), 9 pages.
A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012 ), 10 pages.
H. Aydi, A. Felhi, S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Math. Sci. (Springer), 9 (2015), 103–108.
H. Aydi, E. Karapınar, Fixed point results for generalized \(\alpha-\psi\)-contractions in metric-like spaces and applications, Electron. J. Differential Equations, 2015 (2015 ), 15 pages.
H. Aydi, E. Karapınar, S. Rezapour, A generalized Meir-Keeler-type contraction on partial metric spaces, Abstr. Appl. Anal., 2012 (2012 ), 10 pages.
R. D. Daheriya, R. Jain, M. Ughade, Some fixed point theorem for expansive type mapping in dislocated metric space, ISRN Math. Anal., 2012 (2012 ), 5 pages.
A. Fulga, A. M. Proca, Fixed points for \(\varphi_E\)-Geraghty contractions, Abstr. Appl. Anal., (In press),
R. George, R. Rajagopalan, S. Vinayagam, Cyclic contractions and fixed points in dislocated metric spaces, Int. J. Math. Anal. (Ruse), 9 (2013), 403–411.
V. Gupta, W. Shatanawi, N. Mani, Fixed point theorems for (\(\psi,\beta\))-Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations , J. Fixed Point Theory Appl., 2016 (2016 ), 17 pages.
P. Hitzler, A. K. Seda, Dislocated topologies, J. Electr. Eng., 51 (2000), 3–7.
N. Hussain, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed points of contractive mappings in b-metric-like spaces, Scientific World J., 2014 (2014 ), 15 pages.
A. Isufati , Fixed point theorems in dislocated quasi-metric space, Appl. Math. Sci. (Ruse), 5 (2010), 217–233.
E. Karapınar, H. H. Alsulami, M. Noorwali, Some extensions for Geragthy type contractive mappings, Fixed Point Theory Appl., 2015 (2015 ), 22 pages.
E. Karapınar, H. Aydi, A. Felhi, S. Sahmim, Hausdorff metric-like, generalized Nadler’s Fixed Point Theorem on Metric- Like Spaces and application, Miskolc Math. Notes, (),
E. Karapınar, P. Salimi, Dislocated metric space to metric spaces with some fixed point theorems, Fixed Point Theory Appl. , 2013 (2013 ), 19 pages.
P. S. Kumari, Some fixed point theorems in generalized dislocated metric spaces, Math. Theory Model., 1 (2011), 16–22.
P. S. Kumari, V. V. Kumar, I. Rambhadra Sarma, Common fixed point theorems on weakly compatible maps on dislocated metric spaces , Math. Sci. (Springer), 6 (2012), 5 pages.
S. G. Matthews, Partial metric topology, Papers on general topology and applications,/ Flushing, NY, (1992), Ann. New York Acad. Sci., New York Acad. Sci., New York, 728 (1994), 183–197.
I. R. Sarma, P. S. Kumari, On dislocated metric spaces, Int. J. Math. Arch., 1 (2012), 72–77.
W. Shatanawi, M. S. MD. Noorani, H. Alsamir, A. Bataihah, Fixed and common fixed point theorems in partially ordered quasi-metric spaces, J. Math. Computer Sci., 16 (2016), 516–528.
R. Shrivastava, Z. K. Ansari, M. Sharma , Some results on fixed points in dislocated and dislocated quasi-metric spaces, J. Adv. Stud. Topol., 3 (2012), 25–31.
M. Shrivastava, K. Qureshi, A. D. Singh, A fixed point theorem for continuous mapping in dislocated quasi-metric spaces, Int. J. Theor. Appl. Sci., 4 (2012), 39–40.
K. Zoto, E. Hoxha, A. Isufati, Some new results in dislocated and dislocated quasi-metric spaces, Appl. Math. Sci. (Ruse), 6 (2012), 3519–3526.