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Relation Contractive Selfmaps Involving Cauchy Sequences
Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Napoli, Italy
Dipartimento di Architettura, Centro Interdipartimentale di Ricerca “A. Calza Bini”, Università degli Studi di Napoli Federico II, Napoli, Italy
- 1 Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Napoli, Italy
- 2 Dipartimento di Architettura, Centro Interdipartimentale di Ricerca “A. Calza Bini”, Università degli Studi di Napoli Federico II, Napoli, Italy
Advances in Pure Mathematics·Volume 09 (2019)·Pages 421–428·Published 17 May 2019·DOI10.4236/apm.2019.95020
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Abstract
We obtain two generalizations of a known theorem of A. Alam and M. Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702) showing that some standard proofs can be obtained involving only Cauchy sequences of the successive approximations. Suitable examples prove the effective generalization of our results in metric spaces not necessarily complete.
KeywordsCauchy Sequence<i>d</i>-Self-Closed RelationRelation ContractionRelation Preserving
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