A remark on discontinuity at fixed point

Ravindra K. Bisht; R. P. Pant

doi:10.1016/j.jmaa.2016.02.053

A remark on discontinuity at fixed point

Ravindra K. Bisht
, R. P. Pant

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

72 Citations (Scopus)

Abstract

In this note we give one more solution to the open question of the existence of contractive definitions which are strong enough to generate a fixed point but which do not force the mapping to be continuous at the fixed point (R. Kannan, 1969 [9]; B.E. Rhoades, 1988 [14]).

Original language	English
Pages (from-to)	1239-1242
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	445
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.02.053
Publication status	Published - 15 Jan 2017
Externally published	Yes

Keywords

(ϵ−δ) contractions
Fixed point
ϕ-contractions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.02.053

Cite this

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title = "A remark on discontinuity at fixed point",

abstract = "In this note we give one more solution to the open question of the existence of contractive definitions which are strong enough to generate a fixed point but which do not force the mapping to be continuous at the fixed point (R. Kannan, 1969 [9]; B.E. Rhoades, 1988 [14]).",

keywords = "(ϵ−δ) contractions, Fixed point, ϕ-contractions",

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note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

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doi = "10.1016/j.jmaa.2016.02.053",

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AU - Bisht, Ravindra K.

AU - Pant, R. P.

PY - 2017/1/15

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N2 - In this note we give one more solution to the open question of the existence of contractive definitions which are strong enough to generate a fixed point but which do not force the mapping to be continuous at the fixed point (R. Kannan, 1969 [9]; B.E. Rhoades, 1988 [14]).

AB - In this note we give one more solution to the open question of the existence of contractive definitions which are strong enough to generate a fixed point but which do not force the mapping to be continuous at the fixed point (R. Kannan, 1969 [9]; B.E. Rhoades, 1988 [14]).

KW - (ϵ−δ) contractions

KW - Fixed point

KW - ϕ-contractions

UR - https://www.scopus.com/pages/publications/84961124360

U2 - 10.1016/j.jmaa.2016.02.053

DO - 10.1016/j.jmaa.2016.02.053

M3 - Article

AN - SCOPUS:84961124360

SN - 0022-247X

VL - 445

SP - 1239

EP - 1242

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A remark on discontinuity at fixed point

Abstract

Keywords

ASJC Scopus subject areas

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