Presic Type Operators for a Pair Mappings

Abstract

In this study, we extended the Presic type contraction mapping using $(\delta, L)$-weak contractive. We investigate Presic type weak contraction mapping and obtain some fixed point results in Presic type weak (almost) contraction mappings for a pair of mappings using Jungck type mappings. Additionally, we establish an example to show that the new results are applicable.

Keywords

• Fixed point
• metric spaces
• Presic type almost contractive

References

1. [1] Banach, S., Sur les operations dans les ensembles abstracits et leur application aux equations integrales, Fund. Math., 3(1922), 133-181.
2. [2] Berinde, V., On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19(1)(2003), 7-22.
3. [3] Berinde, V., Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9(1)(2004), 43-53.
4. [4] Berinde, V., Iterative Approximation of Fixed Points, Springer-Verlag, Berlin Heidelberg, 2007.
5. [5] Ciric, L.B., Presic, S.B., On Presic type generalization of the Banach contraction mapping principle, Acta Math Univ Comenianae, 76(2007), 143-147.
6. [6] Jungck, G., Commuting mappings and fixed points, The American Mathematical Monthly, 83(4)(1976), 261-263.
7. [7] Nazır, T., Abbas, M., Common fixed point of Presic type contraction mappings in partial metric spaces, Journal of Nonlinear Analysis and Optimization, 5(2013), 49-55.
8. [8] Pacular, M., Common fixed points for almost Presic type operators, Carpathian J. Math., 28 (1)(2012), 117-126.

9. [9] Presic, S.B., Sur une classe di’n equations aux dierence finite et. sur la convergence de certains suites, Publ de L’Inst Math., 5(1965), 75-78.
10. [10] Rao, K.P.R., Mustaq Ali, Md., Fisher, B., Some Presic Type Generalizations of the Banach Contraction Principle, Mathematica Moravica, 15(1)(2011), 41-47.
11. [11] Shukla, S., Sen, R., Radenovisc, S., Set-Valued Presic type contraction in metric spaces, Annals of the ”Alexandru Ioan Cuza” University of Iasi (New Series). Mathematics, 61(2)(2015), 391-399.
12. [12] Shukla, S., Set-Valued Presic-Chatterjea Type Contractions and Fixed Point Theorems, Gazi University Journal of Science, 29(2)(2016), 473- 478.