Submitted:
12 September 2018
Posted:
13 September 2018
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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.
Keywords:
Cauchy sequence
; d-self-closed relation
; relation contraction
; relation preserving
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