scholarly journals Fixed Point Problems in Cone Rectangular Metric Spaces with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Muhammad Nazam ◽  
Anam Arif ◽  
Hasan Mahmood ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Implicit Relation ◽  
Rectangular Metric Space ◽  
Homotopy Result

In this paper, we introduce an ordered implicit relation and investigate some new fixed point theorems in a cone rectangular metric space subject to this relation. Some examples are presented as illustrations. We obtain a homotopy result as an application. Our results generalize and extend several fixed point results in literature.

scholarly journals Fixed Point Theorems on Generalized Rectangular Metric Spaces

2021 ◽  
Vol 65 (1) ◽  
pp. 59-84
Author(s):  
O. K. Adewale ◽  
◽  
J. O. Olaleru ◽  
H. Olaoluwa ◽  
H. Akewe
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Rectangular Metric Space

In this paper, we introduce the notion of generalized rectangular metric spaces which extends rectangular metric spaces introduced by Branciari. Analogues of the some well-known fixed point theorems are proved in this space. With an example, it is shown that a generalized rectangular metric space is neither a G-metric space nor a rectangular metric space. Our results generalize many known results in fixed point theory.

scholarly journals Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Lokesh Budhia ◽  
Hassen Aydi ◽  
Arslan Hojat Ansari ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
Existence Of A Solution ◽  
Rectangular Metric Space ◽  
Functional Differential

In this paper, we establish some new fixed point theorems for generalized ϕ–ψ-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of C-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay. 

scholarly journals Fixed Point Theorems in Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ismat Beg ◽  
Shaban Sedghi ◽  
Nabi Shobe
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Implicit Relation ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

We prove a fixed point theorem for mappings satisfying an implicit relation in a complete fuzzy metric space.

scholarly journals Coupled fixed point theorems for weakly compatible mappings along with $CLR$ property in Menger metric spaces

2016 ◽  
Vol 8 (2) ◽  
pp. 195-210
Author(s):  
L. Ben Aoua ◽  
A. Aliouche
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Fixed Point Problems ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Menger Metric Space

Coupled fixed point problems have attracted much attention in recent times. The aim of this paper is to extend the notions of E.A. property, CLR property and JCLR property for coupled mappings in Menger metric space and use this notions to generalizes the recent results of Jian-Zhong Xiao. The main result is supported by a suitable example.

scholarly journals Some results in cone metric spaces with applications in homotopy theory

2020 ◽  
Vol 18 (1) ◽  
pp. 295-306 ◽  
Author(s):  
Muhammad Nazam ◽  
Anam Arif ◽  
Hasan Mahmood ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Homotopy Theory ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Self ◽  
Cone Metric Spaces ◽  
Implicit Relation ◽  
Contractive Mappings ◽  
Homotopy Result ◽  
Cone Metric

Abstract The self-mappings satisfying implicit relations were introduced in a previous study [Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacău 7 (1997), 129–133]. In this study, we introduce self-operators satisfying an ordered implicit relation and hence obtain their fixed points in the cone metric space under some additional conditions. We obtain a homotopy result as an application.

The existence theorem of a new multi-valued mapping in metric space endowed with graph

2017 ◽  
Vol 33 (2) ◽  
pp. 191-198
Author(s):  
ARAYA KHEAWBORISUT ◽  
◽  
SUTHEP SUANTAI ◽  
ATID KANGTUNYAKARN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Directed Graph ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Ordered Metric Spaces ◽  
New Type

In this paper, we introduce a new type of multi-valued G-contraction mapping on a metric space endowed with a directed graph G and prove an existence theorem for fixed point problems in metric space endowed with a graph. Moreover, we prove fixed point theorems in partially ordered metric spaces by our main result. Some examples illustrating our main results are also present.

scholarly journals PARTIAL b_{v}(s), PARTIAL v-GENERALIZED AND b_{v}(θ) METRIC SPACES AND RELATED FIXED POINT THEOREMS

2020 ◽  
pp. 621
Author(s):  
Ibrahim Karahan ◽  
Irfan Isik
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Rectangular Metric Space

In this paper, we have introduced three new generalized metric spaces called partial $b_{v}\left( s\right) $, partial $v$-generalized and $b_{v}\left(\theta \right) $ metric spaces which extend $b_{v}\left( s\right) $ metricspace, $b$-metric space, rectangular metric space, $v$-generalized metricspace, partial metric space, partial $b$-metric space, partial rectangular $%b $-metric space and so on. We have proved some famous theorems such as Banach, Kannan and Reich fixed point theorems in these spaces. Also, we have given somenumerical examples to support our definitions. Our results generalize several corresponding results in literature.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

scholarly journals Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Rectangular Metric Space ◽  
New Type ◽  
Symmetry Requirement ◽  
Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

Sign in / Sign up

Export Citation Format

Share Document