Coincidence and common fixed point results via simulation functions in G-metric spaces
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Authors
Manoj Kumar
- Department of Mathematics, Starex University, Gurugram, India.
Sahil Arora
- Department of Mathematics, Lovely Professional University, Punjab, India.
Mohammad Imdad
- Department of Mathematics, Aligarh Muslim University, Aligarh, India.
Waleed M. Alfaqih
- Department of Mathematics, Lovely Professional University, Punjab, India.
Abstract
In this work, we establish some coincidence and common fixed point theorems in symmetrical G-metric space via simulation functions. In the presented work, we extend the results of Argoubi et al. [H. Argoubi, B. Samet, C. Vetro, J. Nonlinear Sci. Appl., \(\bf 8\) (2015), 1082--1094] by using the concept of G-metric space. An illustrative example is also given to show the genuineness of our results. We also apply our results to derive some coincidence and common fixed point results for right monotone simulation function in the framework of G-metric space.
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ISRP Style
Manoj Kumar, Sahil Arora, Mohammad Imdad, Waleed M. Alfaqih, Coincidence and common fixed point results via simulation functions in G-metric spaces, Journal of Mathematics and Computer Science, 19 (2019), no. 4, 288--300
AMA Style
Kumar Manoj, Arora Sahil, Imdad Mohammad, Alfaqih Waleed M., Coincidence and common fixed point results via simulation functions in G-metric spaces. J Math Comput SCI-JM. (2019); 19(4):288--300
Chicago/Turabian Style
Kumar, Manoj, Arora, Sahil, Imdad, Mohammad, Alfaqih, Waleed M.. "Coincidence and common fixed point results via simulation functions in G-metric spaces." Journal of Mathematics and Computer Science, 19, no. 4 (2019): 288--300
Keywords
- Simulation function
- right monotone simulation function
- G-metric space
- coincident point
- fixed point
MSC
References
-
[1]
R. P. Agarwal, Z. Kadelburg, S. Radenović, On coupled fixed point results in asymmetric $g$-metric spaces, J. Inequal. Appl., 2013 (2013), 12 pages
-
[2]
R. P. Agarwal, E. Karapınar, A. F. Roldán-López-de Hierro, Fixed Point Theory in Metric Type Spaces, Springer, Cham (2015)
-
[3]
R. P. Agarwal, E. Karapınar, A. F. Roldán-López-de Hierro, Last remarks on G-metric spaces and related fixed point theorems, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 110 (2016), 433--456
-
[4]
W. M. Alfaqih, R. Gubran, M. Imdad, Coincidence and Common Fixed Point Results under Generalized $(A, S)_f$-Contractions, Filomat, 32 (2018), 2651--2666
-
[5]
H. H. Alsulami, E. Karapınar, F. Khojasteh, A. F. Roldán-López-de Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dyn. Nat. Soc., 2014 (2014), 10 pages
-
[6]
H. Argoubi, B. Samet, C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (2015), 1082--1094
-
[7]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133--181
-
[8]
D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458--464
-
[9]
M. Imdad, W. M. Alfaqih, I. A. Khan, Weak $\theta$-contractions and some fixed point results with applications to fractal theory, Adv. Difference Equ., 2018 (2018), 18 pages
-
[10]
M. Jleli, B. Samet, A new generalization of the banach contraction principle, J. Inequal. Appl., 2014 (2014), 8 pages
-
[11]
E. Karapınar, Fixed points results via simulation functions, Filomat, 30 (2016), 2343--2350
-
[12]
E. Karapınar, A. F. Roldán-López-de Hierro, B. Samet, Matkowski theorems in the context of quasi-metric spaces and consequences on $G$-metric spaces, An. Ştiinţ. Univ. "Ovidius" Constanţa Ser. Mat., 24 (2016), 309--333
-
[13]
F. Khojasteh, V. Rakočević, Some new common fixed point results for generalized contractive multi-valued non-self-mappings, Appl. Math. Lett., 25 (2012), 287--293
-
[14]
F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189--1194
-
[15]
J. Matkowski, Integrable solutions of functional equations, Dissertationes Math. (Rozprawy Mat.), 127 (1975), 68 pages
-
[16]
N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), 177--188
-
[17]
Z. Mustafa, A New Structure for Generalized Metric Spaces: With Applications to Fixed Point Theory, Ph.D. thesis (University of Newcastle), Newcastle (2005)
-
[18]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289--297
-
[19]
O. Popescu, Some new fixed point theorems for $\alpha$-geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 12 pages
-
[20]
B. E. Rhoades, Some theorems on weakly contractive maps, Proceedings of the Third World Congress of Nonlinear Analysts, Part 4 (Catania, 2000). Nonlinear Anal., 47 (2001), 2683--2693
-
[21]
A. F. Roldán-López-de Hierro, E. Karapınar, C. Roldán-López-de Hierro, J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), 345--355
-
[22]
D. Wardowski, N. Van Dung, Fixed points of $F$-weak contractions on complete metric spaces, Demonstr. Math., 47 (2014), 146--155
