Fixed Points and Continuity of Contractive Maps

The aim of this paper is to generalize celebrated results due to Boydand Wong [2] and Matkowski [9] and also to provide yet new solutions to the once open problem on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point. Besides continuous mapp...

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Bibliographic Details
Published in:Filomat 2017-01, Vol.31 (11), p.3501-3506
Main Authors: Pant, Abhijit, Pant, R. P.
Format: Article
Language:English
Subjects:
Diagonal lemma
Function discontinuity
Integers
Mathematical discontinuity
Mathematical functions
Mathematical theorems
Open intervals
Real numbers
Uniqueness
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Summary:The aim of this paper is to generalize celebrated results due to Boydand Wong [2] and Matkowski [9] and also to provide yet new solutions to the once open problem on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point. Besides continuous mappings our results also apply to discontinuous mappings which include threshold operations that are integral part of many a phenomena.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1711501P