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On some recent fixed point results for single and multi-valued mappings in b-metric spaces

Aleksić S., Mitrović Z. D., Radenović S.

Fasciculi Mathematici

2018

Nr 61

5--16

The main purpose of this paper is to improve and correct some results in b-metric spaces. Moreover, we prove that some results can be slightly relaxed and also we explore some proof techniques which provide short proofs of the results.

Fixed point theorems using diameters of level sets and the notion of R.G.I. mapping

Akkouchi M.

Demonstratio Mathematica

2002

Vol. 35, nr 3

621-628

In this paper, we generalize and improve a recent result established by W. A. Kirk and L. M. Saliga (see [3], Theorem 4.3, p. 149) by using a result of W. Walter (see [4]). Indeed, We prove that the conclusions of Kirk-Saliga theorem are not only satisfied but, moreover, they are equivalent for a wide class of contractive gauge functions. Our main result contains also a new equivalent conclusion (see Property (4) in Theorem 2.2 below). As a consequence, we recapture (and improve the results of) a theorem proved by M. Angrisani and M. Clavelli in [2]. Theorem 2.2 completes and improves the main result of[1].