C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces

Abstract

In this paper, we prove fixed point results employing mixed weakly monotone maps, C-class functions and altering distance function in the framework of S-metric space. Here, integral application has additionally been given.

Keywords

• fixed point,S-metric space,mixed weakly monotone property

References

1. Ansari, A.H. , Note on ϕ-ψ- -contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University (2014), 377--380.
2. Dhage, B.C., Generalized metric spaces and mapping with fixed point, Bull. Calcutta Math. Soc. 84 (1992), 329--336.
3. Fisher, B., A fixed point mapping, Bull. Calcutta Math. Soc. 68 (1976), 265--266.
4. Delbosco, D., Un'estensione di un teorema sul punto di S. Reich, Rend. Sem. Mat. Univers. Politecn. Torino 35 (1967), 233--238.
5. Guo, D. and Lakshmikantham, V., Coupled fixed points of nonlinear operators with applications, Nonlinear Analysis 11 (1987), 623--632.
6. Skof, F., Teorema di punti fisso per applicazioni negli spazi metrici, Atti Accad. Sci. Torino 111 (1977), 323--329.
7. Babu, G.V.R. and Sailaja, P.D., A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai Journal of Mathematics 9(1) (2011), 1--10.
8. Sastry, K.P.R., Babu, G.V.R. and Rao, D.N., Fixed point theorem in complete metric space by using a continuous control function, Bull. Cal. Math. Soc. 91(6) (1999), 493--502.

9. Sastry, K.P.R., Naidu, S.V.R., Babu, G.V.R. and Naidu, G.A., Generalization of common fixed point theorems for weakly commuting maps by altering distances, Tamkang J. Math. 31(3) (2000), 243--250.
10. Gordji, M.E., Akbartabar, E., Cho, Y.J. and Remezani, M., Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory and Applications 95 (2012), Article ID:95.
11. Khan, M.S., Swalesh, M. and Sessa, S., Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), 323--326.
12. Dung, N.V., On coupled common fixed points for mixed weakly monotone maps in partially ordered S -metric spaces, Fixed Point Theory and Applications 48 (2013), 17 pages.
13. Mani, N., Existence of fixed points and their applications in certain spaces [Ph.D.Thesis], M. M. University, Mullana, Ambala, India, 2017.
14. Mani, N., Generalized C_{β}^{ψ} -rational contraction and fixed point theorem with application to second order differential equation, Mathematica Moravica 22(1) (2018), 43--54.
15. Marr, R. D., Partially ordered space and metric spaces, American Mathematical Monthly 72(6) (1965), 628--631.
16. Gahler, S., 2-metricsche Raume und ihre topologische structure, Math. Nachr. 26 (1963), 115--148.
17. Sedghi, S., Shobe, N. and Zhou, H., A common fixed point theorem in D -metric spaces, Fixed Point theory and Application 2007 (2007), Article ID 27906, 13 pages.
18. Sedghi, S. and Shobe, N., A common unique random fixed point theorems in S -metric spaces, Journal of Prime Research in Mathematics 7 (2011), 25--34.
19. Sedghi, S. and Shobe, N. and Aliouche, A., A generalizations of fixed point theorems in S -metric spaces, Matematnhpn Bechnk 64 (2012), no. 3, 258--266.
20. Chang, S.S., Cho, Y.J. and Huang, N.J., Coupled fixed point theorems with applications, J. Korean Math. Soc. 33 (1996), no. 3, 575--585.
21. Gupta, V. and Mani, N., Common fixed point for two self-maps satisfying a generalized ^{ψ}∫_{φ} weakly contractive condition of integral type, International Journal of Nonlinear Science, 16(1) (2013), 64--71.
22. Gupta, V., Ramandeep, Mani, N. and Tripathi, A. K., Some fixed point result involving generalized altering distance function, Procedia Computer Science 79 (2016), 112--117.
23. Gupta, V., Shatanawi, W. and Mani, N., Fixed point theorems for (ψ,β) -Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations, J. Fixed Point Theory Appl. 19(2) (2016), 1251--1267.
24. Lakshmikantham, V. and Ciric, L., Coupled common fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70 (2009), 4341--4349.
25. Chen, Y.Z., Existence theorems of coupled fixed points, J. Math. Anal. Appl. 154 (1991), 142--150.
26. Mustafa, Z. and Sims, B., A new approach to generalized metric spaces, J. Nonlinear and Convex Anal. 7(2) (2006), 289--297.