Preprint Article Version 1 This version is not peer-reviewed

Relation Contractive Selfmaps Involving Cauchy Sequences

Version 1 : Received: 12 September 2018 / Approved: 13 September 2018 / Online: 13 September 2018 (03:16:34 CEST)

How to cite: Diviccaro, M.L.; Sessa, S. Relation Contractive Selfmaps Involving Cauchy Sequences. Preprints 2018, 2018090226 (doi: 10.20944/preprints201809.0226.v1). Diviccaro, M.L.; Sessa, S. Relation Contractive Selfmaps Involving Cauchy Sequences. Preprints 2018, 2018090226 (doi: 10.20944/preprints201809.0226.v1).

Abstract

We obtain two generalizations of a known theorem of A. Alam and M. Imdad (Fixed Point Theory Appl. 17 (2015) 693–702) showing that some standard proofs can be obtained involving only Cauchy sequences of the successive approximations instead of the usual successive approximations sequences. Suitable examples prove the effective generalization of our results in metric spaces not necessarily complete.

Subject Areas

Cauchy sequence; d-self-closed relation; relation contraction; relation preserving

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