TITLE:
Relation Contractive Selfmaps Involving Cauchy Sequences
AUTHORS:
Maria Luigia Diviccaro, Salvatore Sessa
KEYWORDS:
Cauchy Sequence, d-Self-Closed Relation, Relation Contraction, Relation Preserving
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.5,
May
17,
2019
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.