scholarly journals Fixed Point of Generalized Weak Contraction in b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Maryam Iqbal ◽  
Afshan Batool ◽  
Ozgur Ege ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Generalized Weak Contraction

In this manuscript, a class of generalized ψ , α , β -weak contraction is introduced and some fixed point theorems in the framework of b -metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.

Fixed point theorems for generalized weak contraction mapping in generating space of b-dislocated metric spaces

2020 ◽  
pp. 2150120
Author(s):  
Reena Jain
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Dislocated Metric Space ◽  
Generalized Weak Contraction ◽  
Dislocated Metric

In this paper, the concept of generalized weak contraction mapping in the setting of generating space of [Formula: see text]-dislocated metric space endowed with partial order is introduced and some fixed-point theorems for the mappings in space satisfying the generalized weak contraction are proved. Example is also given in order to justify our main result.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

scholarly journals Φ,Ψ-Weak Contractions in Neutrosophic Cone Metric Spaces via Fixed Point Theorems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wadei F. Al-Omeri ◽  
Saeid Jafari ◽  
Florentin Smarandache
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weak Contraction ◽  
Cone Metric Spaces ◽  
Altering Distance ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In this manuscript, we obtain common fixed point theorems in the neutrosophic cone metric space. Also, notion of Φ,Ψ-weak contraction is defined in the neutrosophic cone metric space by using the idea of altering distance function. Finally, we review many examples of cone metric spaces to verify some properties.

scholarly journals Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

scholarly journals Fixed point results for weak contractions in partially ordered b-metric space

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
N. Seshagiri Rao ◽  
K. Kalyani ◽  
K. Prasad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contraction Condition ◽  
Generalized Weak Contraction ◽  
Coupled Coincidence

Abstract Objectives We explore the existence of a fixed point as well as the uniqueness of a mapping in an ordered b-metric space using a generalized $$({\check{\psi }}, \hat{\eta })$$ ( ψ ˇ , η ^ ) -weak contraction. In addition, some results are posed on a coincidence point and a coupled coincidence point of two mappings under the same contraction condition. These findings generalize and build on a few recent studies in the literature. At the end, we provided some examples to back up our findings. Result In partially ordered b-metric spaces, it is discussed how to obtain a fixed point and its uniqueness of a mapping, and also investigated the existence of a coincidence point and a coupled coincidence point for two mappings that satisfying generalized weak contraction conditions.

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 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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