Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations

2014 ◽  
Vol 52 (1) ◽  
Author(s):  
Hemant Kumar Nashine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Functional Equations ◽  
Uniqueness Of Solutions ◽  
System Of Functional Equations ◽  
Altering Distance ◽  
Common Limit ◽  
Common Limit Range Property

AbstractThe aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.

scholarly journals Common Fixed Point Theorems in Fuzzy Metric Spaces Satisfying -Contractive Condition with Common Limit Range Property

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Sunny Chauhan ◽  
M. Alamgir Khan ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric ◽  
Common Limit ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The objective of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to our main result, we prove an integral-type fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012).

scholarly journals Common fixed point theorem of six self-mappings in Menger spaces using (CLRST) property

2018 ◽  
Vol 16 (1) ◽  
pp. 1423-1434 ◽  
Author(s):  
Xiao-lan Liu ◽  
Mi Zhou ◽  
Lakshmi Narayan Mishra ◽  
Vishnu Narayan Mishra ◽  
Boško Damjanović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Menger Spaces ◽  
Common Limit ◽  
The Common ◽  
Common Limit Range Property ◽  
Common Fixed Point Theorem

AbstractIn this paper, we study the existence and uniqueness of common fixed point of six self-mappings in Menger spaces by using the common limit range property (denoted by (CLRST)) of two pairs. 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 AN INTEGRAL TYPE COMMON FIXED POINT THEOREM IN DISLOCATED METRIC SPACE

2016 ◽  
Vol 12 (2) ◽  
pp. 60-70
Author(s):  
Dinesh Panthi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Weakly Compatible ◽  
Dislocated Metric Space ◽  
Common Limit ◽  
Common Limit Range Property ◽  
Dislocated Metric ◽  
Common Fixed Point Theorem

 In this article, we establish a common fixed point theorem for two pairs of weakly compatible mappings with common limit range property in dislocated metric space.Mathematics Subject Classification: 47H10, 54H25Kathmandu UniversityJournal of Science, Engineering and TechnologyVol. 12, No. 2, 2016, page: 60-70 

scholarly journals A Hybrid Common Fixed Point Theorem under Certain Recent Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zoran Kadelburg ◽  
Sunny Chauhan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Common Limit ◽  
Hybrid Pair ◽  
Common Limit Range Property ◽  
Common Fixed Point Theorem

We prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings via common limit range property. Our result improves some results from the existing literature, especially the ones contained in Sintunavarat and Kumam (2009). Some illustrative and interesting examples to highlight the realized improvements are also furnished.

A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation

2018 ◽  
Vol 68 (3) ◽  
pp. 655-666
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integral Type ◽  
Implicit Relation ◽  
Contractive Mappings ◽  
Common Limit ◽  
New Type ◽  
Common Limit Range Property

AbstractIn this paper a general fixed point theorem for mappings with a new type of common limit range property satisfying a mixed implicit relation is proved. In the last part of the paper, as application, some fixed point results for mappings satisfying contractive conditions of integral type and forφ-contractive mappings are obtained.

scholarly journals Fixed Point Theorems for Two Pairs of Mappings Satisfying a New Type of Common Limit Range Property in Gp Metric Spaces

2018 ◽  
Vol 32 (1) ◽  
pp. 295-312
Author(s):  
Valeriu Popa ◽  
Alina-Mihaela Patriciu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Contractive Mappings ◽  
Common Limit ◽  
New Type ◽  
Common Limit Range Property

Abstract The purpose of this paper is to prove a general fixed point theorem for mappings involving almost altering distances and satisfying a new type of common limit range property in Gpmetric spaces. In the last part of the paper, some fixed point results for mappings satisfying contractive conditions of integral type and for ⱷ-contractive mappings are obtained.

scholarly journals Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Imdad ◽  
Sunny Chauhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Implicit Function ◽  
Common Limit ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008). As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008). We also furnish some illustrative examples to support our main results.

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