Fixed points and continuity of contractive maps

Abhijit Pant; R. P. Pant

doi:10.2298/FIL1711501P

Fixed points and continuity of contractive maps

Abhijit Pant, R. P. Pant

Kumaun University India

Research output: Contribution to journal › Article › peer-review

84 Citations (Scopus)

Abstract

The aim of this paper is to generalize celebrated results due to Boyd and 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.

Original language	English
Pages (from-to)	3501-3506
Number of pages	6
Journal	Filomat
Volume	31
Issue number	11
DOIs	https://doi.org/10.2298/FIL1711501P
Publication status	Published - 2017
Externally published	Yes

Keywords

Contractive condition
Fixed point
K-continuity
Non-expansive mapping
Threshold operation
Upper semi-continuous

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL1711501P

Cite this

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abstract = "The aim of this paper is to generalize celebrated results due to Boyd and 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.",

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AB - The aim of this paper is to generalize celebrated results due to Boyd and 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.

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KW - Fixed point

KW - K-continuity

KW - Non-expansive mapping

KW - Threshold operation

KW - Upper semi-continuous

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DO - 10.2298/FIL1711501P

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Fixed points and continuity of contractive maps

Abstract

Keywords

ASJC Scopus subject areas

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