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A note on some recent fixed point results for cyclic contractions in \(b\)-metric spaces and an application to integral equations. (English) Zbl 1410.47024

Summary: In this paper, we obtain some equivalences between cyclic contractions and non-cyclic contractions in the framework of \(b\)-metric spaces. Our results improve and complement several recent fixed point results for cyclic contractions in \(b\) -metric spaces established by R. George et al. [“Fixed point theorems for cyclic contractions in \(b\)-metric spaces”, J. Nonlinear Funct. Anal. 2015, Article ID 5, (2015)] and H. K. Nashine and Z. Kadelburg [Filomat 28, No. 10, 2047–2057 (2014; Zbl 1462.54084)]. Moreover, all the results are with much shorter proofs. In addition, an application to integral equations is given to illustrate the usability of the obtained results.

MSC:

47H10 Fixed-point theorems
45G10 Other nonlinear integral equations
54H25 Fixed-point and coincidence theorems (topological aspects)

Citations:

Zbl 1462.54084
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References:

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