Unifying Some Implicit Common Fixed Point Theorems for Hybrid Pairs of Mappings in G-Metric Spaces through Altering Distance Function

2016 ◽  
Vol 10 (5) ◽  
pp. 1787-1798
Author(s):  
Deepak Singh ◽  
Vishal Joshi ◽  
Jong Kyu Kim
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distance Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Altering Distance Function ◽  
Altering Distance ◽  
Common Fixed Point Theorems

scholarly journals Common Fixed Point Theorems in Metric Space by Altering Distance Function

2017 ◽  
Vol 07 (06) ◽  
pp. 335-344
Author(s):  
Vishnu Narayan Mishra ◽  
Balaji Raghunath Wadkar ◽  
Ramakant Bhardwaj ◽  
Idrees A. Khan ◽  
Basant Singh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Altering Distance Function ◽  
Altering Distance ◽  
Common Fixed Point Theorems

scholarly journals Fixed and common fixed point theorems in frame of quasi metric spaces under contraction condition based on ultra distance functions

2018 ◽  
Vol 23 (5) ◽  
pp. 724-748 ◽  
Author(s):  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distance Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Distance Functions ◽  
Type I ◽  
Type Ii ◽  
Contraction Condition ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of ultra distance function. Based on the notion of ultra distance function, we introduce the definitions of (k, ψ, L)-quasi contractions of type (I) and type (II) in the frame of quasi metric spaces. We employ our new definitions to construct and prove many fixed and common fixed point results in the frame of quasi metric spaces. Our results extend and improve many exciting results in the literatures. Also, we introduce some examples and some applications in order to support the usability of our work.

scholarly journals Unified Common Fixed Point Theorems for a Hybrid Pair of Mappings via an Implicit Relation Involving Altering Distance Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sunny Chauhan ◽  
Muhammad Alamgir Khan ◽  
Zoran Kadelburg ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Distance Function ◽  
Altering Distance Function ◽  
Implicit Relation ◽  
Altering Distance ◽  
Hybrid Pair ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The object of this paper is to emphasize the role of a suitable implicit relation involving altering distance function which covers a multitude of contraction conditions in one go. By using this implicit relation, we prove a new coincidence and common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings in a metric space employing the common limit range property. Our main result improves and generalizes a host of previously known results. We also utilize suitable illustrative examples to substantiate the realized improvements in our results.

scholarly journals Fixed point theorems in fuzzy metric spaces for mappings with Bγ,µ condition

2021 ◽  
Author(s):  
Nilakshi Goswami ◽  
Bijoy Patir
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Convergence Results ◽  
Altering Distance

In this paper we prove some fixed point theorems in fuzzy metric spaces for a class of generalized nonexpansive mappings satisfying Bγ,µ condition. We introduce a type of convexity in fuzzy metric spaces with respect to an altering distance function and prove convergence results for some iteration schemes to the fixed point. The results are supported by suitable examples.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

scholarly journals Common fixed point theorems for generalized G- η-χ–contractive type mappings with applications

2017 ◽  
Vol 37 (1) ◽  
pp. 9-20
Author(s):  
Manoj Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of alpha-psi-contractive type mappings in metric spaces. In 2013, Alghamdi et. al. [2] introduced the concept of G-β--contractive type mappings in G-metric spaces. Our aim is to introduce new concept of generalized G-η-χ-contractive pair of mappings. Further, we study some fixed point theorems for such mappings in complete G-metric spaces. As an application, we further establish common fixed point theorems for G-metric spaces for cyclic contractive mappings.

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