Some Presic Type Results in $b-$Dislocated Metric Spaces

Abstract

In this paper, we obtain a Pre\v{s}i\'{c} type common fixed point theorem for four maps in $b$-dislocated metric spaces. We also present one example to illustrate our main theorem. Further, we obtain two more corollaries.

Keywords

• b - Dislocated metric spaces,Jointly 2k - weakly compatible pairs,Pre\v{s}i\'{c} type theorem

References

1. [1] M. Abbas, D. Ilic, T. Nazir, Iterative Approximation of Fixed Points of Generalized Weak Prešic Type k-Step Iterative Method for a Class of Operators, Filomat, 29 (4) (2015) 713-724.
2. [2] R. George, KP Reshma and R. Rajagopalan, A generalised fixed point theorem of Prešic type in cone metric spaces and application to Markov process, Fixed Point Theory Appl., 2011, 2011:85.
3. [3] Z. Kadelburg, S. Radenovic, Notes on Some Recent Papers Concerning F-Contractions in b-Metric Spaces, Constr. Math. Anal., 1(2) (2018), 108-112.
4. [4] E. Karapinar, A Short Survey on the Recent Fixed Point Results on b-Metric Spaces, Constr. Math. Anal., 1(1)(2018) 15-44.
5. [5] A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. 2012, 2012:204
6. [6] P. Hitzler and A. K. Seda, Dislocated topologies, J. Electr. Eng., 51(12) (2000) 3-7.
7. [7] N. Hussain, J. R. Roshan, V. Parvaneh and M. Abbas, Common fixed point results for weak contractive mappings on ordered b-dislocated metric spaces with applications, J. Inequal. Appl., 2013, 2013:486
8. [8] Lj. B. Ciric and S. B. Prešic, On Prešic type generalization of Banach contraction mapping principle, Acta Math. Univ. Comenianae, LXXVI(2) (2007) 143-147.

9. [9] M. Pacurar, Approximating common fixed points of Prešic-Kannan type operators by a multi-step iterative method, An. St. Univ. Ovidius Constanta, 17(1) (2009) 153-168.
10. [10] S. B. Prešic, Sur une classe d’inequations aux differences finite et sur la convergence de certaines suites, Publications de l’Institut Mathématique, 5(19) (1965) 75-78.
11. [11] K. P. R. Rao, G. N. V. Kishore and Md. Mustaq Ali, Generalization of Banach contraction principle of Prešic type for three maps, Math. Sci., 3(3) (2009) 273 - 280.
12. [12] K. P. R. Rao, Md. Mustaq Ali and B.Fisher, Some Preši´c type generalization of Banach contraction principle, Math. Moravica 15 (2011) 41 - 47.
13. [13] P. Salimi, N. Hussain, S. Shukla, Sh. Fathollahi, S. Radenovic, Fixed point results for cyclic $\alpha -\psi \phi -$ contractions with applications to integral equations, J. Comput. Appl. Math., 290 (2015) 445-458.
14. [14] S. Shukla, S. Radenovic, S. Pantelic, Some Fixed Point Theorems for Prešic-Hardy-Rogers Type Contractions in Metric Spaces, Journal of Mathematics, (2013) ArticleID 295093.
15. [15] S. Shukla, S. Radenovic, V.C . Rajic, Some common fixed point theorems in $\sigma -$complete metric-like spaces, Vietnam J. Math., 41 (2013) 341-352.