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 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 Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

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

2022 ◽  
Vol 27 (1) ◽  
pp. 163-178
Author(s):  
Mudasir Younis ◽  
Aleksandra Stretenović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Order ◽  
Metric Spaces ◽  
Functional Differential Equations ◽  
Contractive Condition ◽  
Nonlinear Anal ◽  
Model Control ◽  
Functional Differential ◽  
Picard Sequence

In this manuscript, we generalize, improve, and enrich recent results established by Budhia et al. [L. Budhia, H. Aydi, A.H. Ansari, D. Gopal, Some new fixed point results in rectangular metric spaces with application to fractional-order functional differential equations, Nonlinear Anal. Model. Control, 25(4):580–597, 2020]. This paper aims to provide much simpler and shorter proofs of some results in rectangular metric spaces. According to one of our recent lemmas, we show that the given contractive condition yields Cauchyness of the corresponding Picard sequence. The obtained results improve well-known comparable results in the literature. Using our new approach, we prove that a Picard sequence is Cauchy in the framework of rectangular metric spaces. Our obtained results complement and enrich several methods in the existing state-ofart. Endorsing the materiality of the presented results, we also propound an application to dynamic programming associated with the multistage process.

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 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.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

Coupled coincidence and coupled common fixed point theorems on a fuzzy metric space with a graph

2018 ◽  
Vol 34 (3) ◽  
pp. 417-424
Author(s):  
PHUMIN SUMALAI ◽  
◽  
POOM KUMAM ◽  
DHANANJAY GOPAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric ◽  
Coupled Common Fixed Point ◽  
Common Fixed Point Theorems ◽  
Coupled Coincidence

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1–14], we introduce a new class of G − f−contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph.

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