scholarly journals Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 55
Author(s):  
Kapil Jain ◽  
Jatinderdeep Kaur
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Linear Equations ◽  
Open Problems ◽  
New Class ◽  
Contractive Mappings ◽  
Simultaneous Linear Equations ◽  
Class Of Functions

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

Some fixed point theorems in partial \(S_b\)-metric spaces

2018 ◽  
Vol 9 (1) ◽  
pp. 1
Author(s):  
Koushik Sarkar ◽  
Manoranjan Singha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
New Class ◽  
Contractive Mappings ◽  
Banach Contraction

N. Souayah [10] introduced the concept of partial Sb-metric spaces. In this paper, we established a fixed point theorem for a new class of contractive mappings and a generalization of Theorem 2 from [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Am. Math. Soc. 136, (2008), 1861-1869] in partial Sb-metric spaces. We provide an example in support of our result.

scholarly journals Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Contractive Mappings ◽  
Contractive Type

We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.

scholarly journals A Generalization of a Greguš Fixed Point Theorem in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Marwan A. Kutbi ◽  
A. Amini-Harandi ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Contractive Mappings

We first introduce a new class of contractive mappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theorem in metric spaces and generalize and unify some related results in the literature. An example is also given to support our main result.

scholarly journals On Some Common Fixed Point Results for Weakly Contraction Mappings with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yan Hao ◽  
Hongyan Guan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
New Class ◽  
Contractive Mappings ◽  
Weakly Contractive

In this paper, we introduce a new class of generalized weakly contractive mappings and prove common fixed point results by using different algorithms involving this new class of mappings in the framework of b -metric spaces, which generalize the results of Cho. We also provide two examples to show the applicability and validity of our results. As an application of our result, we obtain a solution to an integral equation. Our results extend and improve several comparable results in the existing literature.

scholarly journals Common fixed points of fuzzy set-valued contractive mappings on metric spaces with a directed graph

2021 ◽  
Vol 7 (2) ◽  
pp. 2195-2219
Author(s):  
Muhammad Rafique ◽  
◽  
Talat Nazir ◽  
Mujahid Abbas ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fuzzy Set ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Fuzzy Mathematics ◽  
New Class ◽  
Contractive Mappings ◽  
New Research

<abstract><p>We introduce a new class of generalized graphic fuzzy $ F $- contractive mappings on metric spaces and establish the existence of common fuzzy coincidence and fixed point results for such contractions. It is significant to note that we do not use any form of continuity of mappings to prove these results. Some examples are provided to verify our proven results. Various developments in the existing literature are generalized and extended by our results. It is aimed that the initiated concepts in this work will encourage new research aspects in fixed point theory and related hybrid models in the literature of fuzzy mathematics.</p></abstract>

scholarly journals Common Fixed Point Results for Generalized g − α s p , ψ , φ Contractive Mappings with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jianju Li ◽  
Hongyan Guan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
New Class ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

In this paper, we introduce a new class of g − α s p − admissible mappings and prove some common fixed point theorems involving this new class of mappings which satisfy generalized contractive conditions in the framework of b − metric spaces. We also provide two examples to show the applicability and validity of our results. Meanwhile, we present an application to the existence of solutions to an integral equation by means of one of our results.

Fuzzy Θf-contractive mappings and their fixed points with applications

2020 ◽  
Vol 39 (5) ◽  
pp. 7097-7106
Author(s):  
Hayel Nasr Saleh ◽  
Mohammad Imdad ◽  
Idrees Khan ◽  
Md Hasanuzzaman
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Present Article ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Auxiliary Function ◽  
Fuzzy Metric Spaces ◽  
New Class ◽  
Contractive Mappings

In the present article, inspired by the work of Jleli et al. [J. Inequal. Appl. 2014, 38 (2014)] and [J. Inequal. Appl. 2014, 439 (2014)] in metric spaces, we proposed a new class of contractive mappings termed as: fuzzy Θf-contractive mappings by using an auxiliary function Θf : (0, 1) → (0, 1) satisfying suitable properties. This class has further been weakened by defining the class of fuzzy Θf-weak contractive mappings to realize yet another class of contractive mappings. Thereafter, these two newly introduced classes of contractive mappings are utilized to establish some fixed point theorems in M-complete fuzzy metric spaces (in the sense of George and Veeramani). In support of our newly obtained results, we provide some examples besides furnishing applications to dynamic programming.

New fixed point results in bv(s)-metric spaces

2020 ◽  
Vol 70 (2) ◽  
pp. 441-452
Author(s):  
Tatjana Došenović ◽  
Zoran Kadelburg ◽  
Zoran D. Mitrović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Contractive Mappings ◽  
Generalized Metric ◽  
The One

Abstract Z. D. Mitrović and S. Radenović introduced in [The Banach and Reich contractions in bv(s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 3087–3095] a new class of generalized metric spaces and proved some fixed point theorems in this framework. The purpose of this paper is to consider other kinds of contractive mappings in bv(s)-metric spaces, and show how the work in the new settings differs from the one in standard metric and b-metric spaces. Examples show the usefulness of the obtained results.

scholarly journals Some new fixed point theorems in complete metric spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 189-196
Author(s):  
M. O. OLATINWO ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Contractive Mappings

In this paper, we obtain some fixed point theorems for more general classes of mappings than the A−contractions of Akram et al. We also give an example of mappings satisfying our new class of contractive mappings but which does not satisfy the contractive condition of Akram et al. Our results generalize and extend the recent results of Akram et al., and unify several other classical results in the literature.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

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