scholarly journals On common fixed points of weakly commuting mappings and set-valued mappings

1986 ◽  
Vol 9 (2) ◽  
pp. 323-329 ◽  
Author(s):  
S. Sessa ◽  
B. Fisher
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Weakly Commuting Mappings ◽  
The Common ◽  
Set Valued Mappings ◽  
Commuting Mappings ◽  
Weak Commutativity

Our main theorem establishes the uniqueness of the common fixed point of two set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author.

scholarly journals Common Fixed Point of TwoR-Weakly Commuting Mappings inb-Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Poom Kumam ◽  
Wutiphol Sintunavarat ◽  
Shaban Sedghi ◽  
Nabi Shobkolaei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Weakly Commuting Mappings ◽  
Commuting Mappings

We prove some common fixed point results for two mappings satisfying generalized contractive condition inb-metric space. Note thatb-metric of main results in this work are not necessarily continuous. So our results extend and improve several previous works. We also present one example that shows the applicability and usefulness of our results.

On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

scholarly journals Common Fixed Point Theorems of Greguš Type (ϕ,ψ)-Weak Contraction for R-Weakly Commuting Mappings in 2-Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Penumarthy Parvateesam Murthy ◽  
Uma Devi Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Weakly Commuting Mappings ◽  
Set Valued Mappings ◽  
Commuting Maps ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Commuting Mappings

The main purpose of this paper is to establish a common fixed point theorem for set valued mappings in 2-metric spaces by generalizing a theorem of Abd EL-Monsef et al. (2009) and Murthy and Tas (2009) by using (ϕ,ψ)-weak contraction in view of Greguš type condition for set valued mappings using R-weakly commuting maps.

scholarly journals Weak Contraction Condition Involving Cubic Terms ofdx,yunder the Fixed Point Consideration

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Penumurthy Parvateesam Murthy ◽  
K. N. V. V. Vara Prasad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Weak Contraction ◽  
Contraction Condition

A fixed point theorem is presented for single-valued map with using generalizedφ-weak contractive condition involving various combinations ofdx,yon a complete metric space. Our result is an extension as well as a generalization of Alber and Guerre-Delabriere (1997) in particular. It also generalizes the results of Rhoades (2001), Choudhury and Dutta, (2000), and Dutta and Choudhury, (2008).

scholarly journals ON Modified(α-η)-Contractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Muhammad Arshad ◽  
Aftab Hussain
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Contractive Mappings

Hussain et al. (2013) established new fixed point results in complete metric space. In this paper, we prove fixed point results ofα-admissible mappings with respect toη, for modified contractive condition in complete metric space. An example is given to show the validity of our work. Our results generalize/improve several recent and classical results existing in the literature.

scholarly journals Results on common fixed points on complete metric spaces

1980 ◽  
Vol 21 (1) ◽  
pp. 165-167 ◽  
Author(s):  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Image Position ◽  
Commuting Mappings ◽  
Unique Common Fixed Point

The following theorem was proved in [1].Theorem 1. Let S and T be continuous, commuting mappings of a complete, bounded metric space (X, d) into itself satisfying the inequalityfor all x, y in X, where 0≤c<1 and p, p′, q, q′≥0 are fixed integers with p+p′, q+q′≥1. Then S and T have a unique common fixed point z. Further, if p′ or q′ = 0, then z is the unique fixed point of S and if p or q = 0, then z is the unique fixed point of T.

scholarly journals Common Fixed Point for Weakly Compatible Maps in Metric Space

1970 ◽  
Vol 3 (2) ◽  
pp. 21-26
Author(s):  
K Jha
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Weakly Compatible ◽  
Engineering And Technology ◽  
Common Fixed Point Theorem

A common fixed point theorem involving two pairs of weakly compatible mappings is proved under a Lipschitz type contractive condition, which is independent of the known contractive definitions. Keywords: fixed point; complete metric space; weakly compatible maps. DOI: 10.3126/kuset.v3i2.2893 Kathmandu University Journal of Science, Engineering and Technology Vol.3, No.2, August 2007, pp 21-26

scholarly journals Common fixed points using (ψ,ϕ ) - type contractive maps in fuzzy metric spaces

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Vishal Gupta ◽  
Manu Verma
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Fuzzy Metric Space ◽  
Contractive Condition ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Control Functions ◽  
Contractive Maps

This In this paper, we define new control functions to give unique fixed point in fuzzy metric space. A fruitful contractive condition of (ψ, ϕ)- type is used to obtain common fixed point theorem for two maps in fuzzy metric spaces. We extend the existing results in metric space to fuzzy metric space using these control functions. The first theorem is the extension of the result of Zhang and Song (2009) under the required contractive conditions. Second result is analogous to the result of Doric (2009) in metric spaces.

scholarly journals Some Fixed Point Results in Function Weighted Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Awais Asif ◽  
Nawab Hussain ◽  
Hamed Al-Sulami ◽  
Muahammad Arshad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Closed Ball ◽  
Contractive Condition ◽  
Banach Contraction ◽  
The Banach Contraction Principle ◽  
Type Contraction ◽  
Unique Common Fixed Point

After the establishment of the Banach contraction principle, the notion of metric space has been expanded to more concise and applicable versions. One of them is the conception of ℱ -metric, presented by Jleli and Samet. Following the work of Jleli and Samet, in this article, we establish common fixed points results of Reich-type contraction in the setting of ℱ -metric spaces. Also, it is proved that a unique common fixed point can be obtained if the contractive condition is restricted only to a subset closed ball of the whole ℱ -metric space. Furthermore, some important corollaries are extracted from the main results that describe fixed point results for a single mapping. The corollaries also discuss the iteration of fixed point for Kannan-type contraction in the closed ball as well as in the whole ℱ -metric space. To show the usability of our results, we present two examples in the paper. At last, we render application of our results.

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