Common Unique Fixed Point Theorems for Compatible Mappings of Type (A) in Complete Metric Space

2014 ◽  
Vol 13 (1) ◽  
pp. 58-67
Author(s):  
Arvind Kumar Sharma ◽  
◽  
V. H Badshah ◽  
V. K Gupta
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Type A ◽  
Compatible Mappings

scholarly journals Some fixed point theorems

1992 ◽  
Vol 53 (3) ◽  
pp. 304-312 ◽  
Author(s):  
P. V. Subrahmanyam ◽  
I. L. Reilly
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contraction Principle ◽  
Carry Over ◽  
Banach's Theorem ◽  
Banach’S Contraction Principle

AbstractBanach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.

scholarly journals Common Fixed Points of Compatible Mappings

2012 ◽  
Vol 4 (3) ◽  
pp. 603-608
Author(s):  
M. P. Singh ◽  
R. Yumnam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Compatible Mappings ◽  
Type B ◽  
Common Fixed Point Theorems

In this paper we prove two common fixed point theorems by considering four mappings in complete metric space. In the first theorem we consider two pairs of compatible mappings of type (A) and in the second theorem we consider two pairs of compatible mappings of type (B). Our results modify and extend some earlier results in the literature.© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v4i3.10567 J. Sci. Res. 4 (3), 603-608 (2012)

scholarly journals Fixed Point Theorems and Iterative Function System in G-Metric Spaces

2019 ◽  
Vol 27 (2) ◽  
pp. 329-340
Author(s):  
Salwa Salman Abed ◽  
Anaam Neamah Faraj
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Generalized Contraction ◽  
Numerical Examples ◽  
Iterated Function ◽  
Self Similar

Iterated function space is a method to construct fractals and the results are self-similar. In this paper, we introduce the Hutchinson Barnsley operator (shortly, operator) on a  metric space and employ its theory to construct a fractal set as its unique fixed point by using Ciric type generalized -contraction in complete metric space. In addition, some concepts are illustrated by numerical examples.

On Fixed Point Theorems in Complete Metric Space

2019 ◽  
Vol 10 (7) ◽  
pp. 1419-1425
Author(s):  
Jayashree Patil ◽  
Basel Hardan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space

Common Fixed Point Theorems Using Compatible Mappings of Type (R) in Semi-metric Space

2020 ◽  
Vol 5 (5) ◽  
pp. 40-44
Author(s):  
Umesh Rajopadhyaya ◽  
K. Jha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we establish a common fixed point theorem for three pairs of self mappings in semi-metric space using compatible mappings of type (R) which improves and extends similar known results in the literature.

Extension of fixed point results in intuitionistic fuzzy b metric space

2020 ◽  
Vol 39 (5) ◽  
pp. 7831-7841
Author(s):  
Nabanita Konwar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Cauchy Sequence ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Intuitionistic Fuzzy ◽  
Contraction Theorem

The aim of this paper is to define the notion of intuitionistic fuzzy b metric space (in short, IFbMS) along with some useful results. We establish some important Lemmas in order to study the Cauchy sequence in IFbMS. To further develop the work, we establish some fixed point theorems and study the existence of unique fixed point of some self mappings in IFbMS. We also develop the concept of Ćirić quasi-Contraction theorem in IFbMS. Examples are provided to validate the non-triviality of the results.

scholarly journals COMMON FIXED POINT THEOREMS FOR COMPATIBLE MAPPINGS OF TYPE (A) IN NON-ARCHIMEDEAN MENGER PM-SPACES

2019 ◽  
pp. 19-25
Author(s):  
Omar Abu-gdere ◽  
M.H.M. Rashid
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Type A ◽  
Compatible Mappings ◽  
Compatible Mapping ◽  
Common Fixed Point Theorems

The aim of this paper is to prove the existence common fixed point for compatible mapping of type (A) in Non-Archimedean Menger PM-space and we introduced new conditions for this type.

scholarly journals Some Results by Using CLR’s-Property in Probabilistic 2-Metric Space

2021 ◽  
Vol 19 (6) ◽  
pp. 904-914
Author(s):  
V. Srinivas ◽  
K. Satyanna
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Weakly Compatible

The aim of this paper is to generate two fixed point theorems in probabilistic 2-metric space by applying CLR’S-property and occasionally weakly compatible mappings (OWC), these two results generalize the theorem proved by V. K. Gupta, Arihant Jain and Rajesh Kumar. Further these results are justified with suitable examples.

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