Orbital continuity and fixed points

Abhijit Pant; R. P. Pant

doi:10.2298/FIL1711495P

Orbital continuity and fixed points

Abhijit Pant, R. P. Pant

Kumaun University India

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

9 Citations (Scopus)

Abstract

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type A_f or of type A_g of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

Original language	English
Pages (from-to)	3495-3499
Number of pages	5
Journal	Filomat
Volume	31
Issue number	11
DOIs	https://doi.org/10.2298/FIL1711495P
Publication status	Published - 2017
Externally published	Yes

Keywords

Coincidence point
Fixed point
Orbital continuity
Quasi R-commuting
Semi R-commuting

ASJC Scopus subject areas

General Mathematics

Access to Document

10.2298/FIL1711495P

Cite this

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AB - The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type Af or of type Ag of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

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KW - Quasi R-commuting

KW - Semi R-commuting

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Orbital continuity and fixed points

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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