Meir-Keeler type and Caristi type fixed point theorems

Abhijit Pant; R. P. Pant; Vladimir Rakočević

doi:10.2298/AADM181224037P

Meir-Keeler type and Caristi type fixed point theorems

Abhijit Pant
, R. P. Pant
, Vladimir Rakočević

Kumaun University India

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

2 Citations (Scopus)

Abstract

Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.

Original language	English
Pages (from-to)	849-858
Number of pages	10
Journal	Applicable Analysis and Discrete Mathematics
Volume	13
Issue number	3
DOIs	https://doi.org/10.2298/AADM181224037P
Publication status	Published - 1 Dec 2019
Externally published	Yes

Keywords

Caristi type maps
Contractive mappings
Fixed point
K-continuity

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.2298/AADM181224037P

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title = "Meir-Keeler type and Caristi type fixed point theorems",

abstract = "Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.",

keywords = "Caristi type maps, Contractive mappings, Fixed point, K-continuity",

author = "Abhijit Pant and Pant, \{R. P.\} and Vladimir Rako{\v c}evi{\'c}",

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year = "2019",

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doi = "10.2298/AADM181224037P",

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T1 - Meir-Keeler type and Caristi type fixed point theorems

AU - Pant, Abhijit

AU - Pant, R. P.

AU - Rakočević, Vladimir

PY - 2019/12/1

Y1 - 2019/12/1

N2 - Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.

AB - Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.

KW - Caristi type maps

KW - Contractive mappings

KW - Fixed point

KW - K-continuity

UR - https://www.scopus.com/pages/publications/85080883579

U2 - 10.2298/AADM181224037P

DO - 10.2298/AADM181224037P

M3 - Article

AN - SCOPUS:85080883579

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VL - 13

SP - 849

EP - 858

JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 3

ER -

Meir-Keeler type and Caristi type fixed point theorems

Abstract

Keywords

ASJC Scopus subject areas

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