A unified common fixed point theorem for a family of mappings

Vijay Dalakoti; Ravindra K. Bisht; R. P. Pant; Mahesh C. Joshi

doi:10.2298/FIL2103759D

A unified common fixed point theorem for a family of mappings

Vijay Dalakoti
, Ravindra K. Bisht
, R. P. Pant
, Mahesh C. Joshi

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

1 Citation (Scopus)

Abstract

The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

Original language	English
Pages (from-to)	759-769
Number of pages	11
Journal	Filomat
Volume	35
Issue number	3
DOIs	https://doi.org/10.2298/FIL2103759D
Publication status	Published - 2021
Externally published	Yes

Keywords

(ɛ − δ)−contraction
Fixed point
Upper-semi continuity
φ− contraction

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL2103759D

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title = "A unified common fixed point theorem for a family of mappings",

abstract = "The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.",

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AU - Dalakoti, Vijay

AU - Bisht, Ravindra K.

AU - Pant, R. P.

AU - Joshi, Mahesh C.

PY - 2021

Y1 - 2021

N2 - The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

AB - The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.

KW - (ɛ − δ)−contraction

KW - Fixed point

KW - Upper-semi continuity

KW - φ− contraction

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DO - 10.2298/FIL2103759D

M3 - Article

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SP - 759

EP - 769

JO - Filomat

JF - Filomat

IS - 3

ER -

A unified common fixed point theorem for a family of mappings

Abstract

Keywords

ASJC Scopus subject areas

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