Fixed points of Suzuki contractive mappings in relational metric spaces. (English) Zbl 1510.54041
Summary: In this paper, we prove an analogous version of fixed point theorem due to T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)] using \(\mathcal{R}\)-sequential limit property and some other relation theoretic metrical variants. The present results generalize well known recent results such as D. Paesano and P. Vetro [Topology Appl. 159, No. 3, 911–920 (2012; Zbl 1241.54035)], A. Alam and M. Imdad [J. Fixed Point Theory Appl. 17, No. 4, 693–702 (2015; Zbl 1335.54040)] and besides many others. Radically, these investigations open another new direction of relational metric fixed point theory. We also present non-trivial example to show the validity and importance of such investigations.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54E40 | Special maps on metric spaces |
References:
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