scholarly journals A New Approach to Common Coupled Fixed Point of Caristi Type Contraction on a Metric Space Endowed with a Graph

2018 ◽  
Vol 7 (4.10) ◽  
pp. 323
Author(s):  
G. Adilakshmi ◽  
G. N.V.Kishore ◽  
N. Konda Reddy
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Complete Metric Space ◽  
Coupled Fixed Point ◽  
Edge Preserving ◽  
New Approach ◽  
Common Coupled Fixed Point ◽  
Type Contraction

In this paper we introduced a new notation G – fg –   contraction of Caristi type and a new edge preserving property. With help of these we proved a some coupled fixed point results for four maps endowed with a graph in a complete metric space. Also we gave an application to integral equations. 

scholarly journals Coupled Fixed Point Theorems in Vector b-metric Space

2019 ◽  
Vol 8 (3S3) ◽  
pp. 468-476
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Common Coupled Fixed Point

This paper consists of some coupled and common coupled fixed point theorems in vector b-metric spaces. Vector b-metric space or E-b-metric space was introduced by Petre [6] merging the concepts of vector metric space as introduced by Cevik [4] and b-metric space as introduced by Czerwik [5]. We generalize the results of Shatnanawi and Hani [8] and Rao et al. [7].

scholarly journals Common Coupled Fixed Point Theorem for Geraghty-Type Contraction in Partially Ordered Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiao-lan Liu ◽  
Mi Zhou ◽  
Boško Damjanović
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Common Coupled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Weakly Compatible ◽  
Common Limit Range Property ◽  
Type Contraction

We study the existence and uniqueness of common coupled fixed point of four self-mappings for Geraghty-type contraction using weakly compatible mappings in partially ordered metric spaces with common limit range property (denoted by (CLRST)), the property of E.A, and so on. It is noted that the continuity of mappings and completeness of spaces can be removed. Our results improve, extend, complement, and generalize several existing results in the literature. Also, some examples are provided to illustrate the usability of our results.

scholarly journals Ciric type generalized F-contractions on completemetric spaces and fixed point results

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1143-1151 ◽  
Author(s):  
Gülhan Mınak ◽  
Asuman Helvacı ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Proper Generalization ◽  
Type Contraction

Recently, Wardowski [15] introduced the concept of F-contraction on complete metric space. This type contraction is proper generalization of ordinary contraction. In the present paper, we give some fixed point results for generalized F-contractions including Ciric type generalized F-contraction and almost F-contraction on complete metric space. Also, we give some illustrative examples.

scholarly journals Orbital continuity and fixed points

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3495-3499 ◽  
Author(s):  
Abhijit Pant ◽  
R.P. Pant
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Sufficient Condition ◽  
Point Property ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Type Contraction

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 A1 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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