scholarly journals A New Study on the Fixed Point Sets of Proinov-Type Contractions via Rational Forms

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 93
Author(s):  
Mi Zhou ◽  
Xiaolan Liu ◽  
Naeem Saleem ◽  
Andreea Fulga ◽  
Nihal Özgür
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Point Sets ◽  
Lower Semi ◽  
Continuity Assumption ◽  
Weaker Conditions ◽  
Fixed Point Sets ◽  
Unique Common Fixed Point

In this paper, we presented some new weaker conditions on the Proinov-type contractions which guarantees that a self-mapping T has a unique fixed point in terms of rational forms. Our main results improved the conclusions provided by Andreea Fulga (On (ψ,φ)−Rational Contractions) in which the continuity assumption can either be reduced to orbital continuity, k−continuity, continuity of Tk, T-orbital lower semi-continuity or even it can be removed. Meanwhile, the assumption of monotonicity on auxiliary functions is also removed from our main results. Moreover, based on the obtained fixed point results and the property of symmetry, we propose several Proinov-type contractions for a pair of self-mappings (P,Q) which will ensure the existence of the unique common fixed point of a pair of self-mappings (P,Q). Finally, we obtained some results related to fixed figures such as fixed circles or fixed discs which are symmetrical under the effect of self mappings on metric spaces, we proposed some new types of (ψ,φ)c−rational contractions and obtained the corresponding fixed figure theorems on metric spaces. Several examples are provided to indicate the validity of the results presented.

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 Cyclic G ‐ Ω -Weak Contraction-Weak Nonexpansive Mappings and Some Fixed Point Theorems in Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sahar Mohamed Ali Abou Bakr
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Nonexpansive Mappings ◽  
Research Paper ◽  
Weak Contraction ◽  
Compact Metric Spaces ◽  
Unique Common Fixed Point

This paper introduces novel concepts of joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak contraction and joint Y , Z cyclic G ‐ Ω S , T , a b e f -weak nonexpansive mappings and then proves the existence of a unique common fixed point of such mappings in case of complete and compact metric spaces, respectively, in particular, it proves the existence of a unique fixed point for both cyclic G ‐ Ω S , a b e f -weak contraction and cyclic G ‐ Ω S , a b e f -weak nonexpansive mappings, and hence, it also proves the existence of a unique fixed point for both cyclic Ω S , a b e f -weak contraction and cyclic Ω S , a b e f -weak nonexpansive mappings. The results of this research paper extend and generalize some fixed point theorems previously proved via the attached references.

scholarly journals Results on common fixed points on complete metric spaces

1980 ◽  
Vol 21 (2) ◽  
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 theorems for contractive mappings satisfying Φ-maps in S-metric spaces

2016 ◽  
Vol 8 (2) ◽  
pp. 298-311 ◽  
Author(s):  
Shaban Sedghi ◽  
Mohammad Mahdi Rezaee ◽  
Tatjana Došenović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Contractive Mappings ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

Abstract In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

scholarly journals A Unique Common Fixed Point for an Infinity of Set-Valued Maps

2018 ◽  
Vol 32 (1) ◽  
pp. 79-97
Author(s):  
Hakima Bouhadjera
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Minimal Type ◽  
Common Fixed Point Theorems ◽  
Unique Common Fixed Point

Abstract The main purpose of this paper is to establish some common fixed point theorems for single and set-valued maps in complete metric spaces, under contractive conditions by using minimal type commutativity and without continuity. These theorems generalize, extend and improve the result due to Elamrani and Mehdaoui ([2]) and others. Also, common fixed point theorems in metric spaces under strict contractive conditions are given.

scholarly journals Some Common Fixed Points of Six Mappings on G_b-metric Spaces Using (E.A) Property

2018 ◽  
Vol 11 (1) ◽  
pp. 90 ◽  
Author(s):  
Zead Mustafa ◽  
M.M.M. Jaradat ◽  
Hassen Aydi ◽  
Ahmad Alrhayyel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

The aim of this manuscript is to present a unique common fixed point theorem for six mappings satisfying $(\phi ,\psi )$-contractions using (E.A) property in the framework of $G_{b}$- metric spaces. An illustrative example is also given to justify the established result.

scholarly journals Unique Common Fixed Point Theorems for Pairs of Hybrid Maps under a New Condition in Partial Metric Spaces

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
K. P. R. Rao ◽  
K. R. K. Rao
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Partial Hausdorff Metric ◽  
Common Fixed Point Theorems ◽  
Unique Common Fixed Point

AbstractIn this paper, we introduce a new condition namely, ‘condition (W.C.C)’ and obtain two unique common fixed point theorems for pairs of hybrid mappings on a partial Hausdorff metric space without using any continuity and commutativity of the mappings.

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