scholarly journals Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Contractive Mapping ◽  
Contraction Mappings ◽  
Weakly Contractive Mapping ◽  
New Concepts ◽  
Weakly Contractive ◽  
Type Contraction

In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of g -interpolative Hardy–Rogers type contractions in b -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.

scholarly journals Fixed Point Results Using Ft-Contractions in Ordered Metric Spaces Having t-Property

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 313 ◽  
Author(s):  
Hassen Aydi ◽  
Tawseef Rashid ◽  
Qamrul Khan ◽  
Zead Mustafa ◽  
Mohammed Jaradat
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Ordered Metric Space ◽  
Ordered Metric Spaces ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
New Concepts

In this paper, we prove the existence of fixed points of F t -contraction mappings in partially ordered metric spaces not necessarily complete. We require that the ordered metric space has the t-property, which is a new concept introduced recently by Rashid et.al. We also give some examples to illustrate the new concepts and obtained results.

scholarly journals Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 132
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Type ◽  
The Given ◽  
Type Contraction

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

scholarly journals Existence of Fixed Point Results in -Metric Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Zead Mustafa ◽  
Wasfi Shatanawi ◽  
Malik Bataineh
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weaker Conditions

The purpose of this paper is to prove the existence of fixed points of contractive mapping defined on -metric space where the completeness is replaced with weaker conditions. Moreover, we showed that these conditions do not guarantee the completeness of -metric spaces.

scholarly journals Weakly Contractive Mapping and Weakly Kannan Mapping in Partial Metric Space

2019 ◽  
Vol 20 (1) ◽  
pp. 33
Author(s):  
S. Sunarsini ◽  
S. Sadjidon ◽  
Annisa Rahmita
Keyword(s):  
Metric Space ◽  
Partial Metric Space ◽  
Contractive Mapping ◽  
Contraction Principle ◽  
Partial Metric ◽  
Weakly Contractive Mapping ◽  
Kannan Mapping ◽  
Cauchy Sequences ◽  
Weakly Contractive ◽  
Banach’S Contraction Principle

In the article the concept of metric space could be expanded, one of which is a partial metric space. In the metric space, the distance of a point to itself is equal to zero, while in the partial metric space need not be equal to zero.The concept of partial metric space is used to modify Banach's contraction principle. In this paper, we discuss weakly contractive mapping and weakly Kannan mapping which are extensions of Banach's contraction principle to partial metric space together some related examples. Additionally, we discuss someLemmas which are shows an analogy between Cauchy sequences in partial metric space with Cauchy sequences in metric space and analogy between the complete metric space and the complete partial metric space. Keywords: Cellulose metric space, partial metric space, weakly contraction mapping, weakly Kannan mapping.

scholarly journals Common fixed points of multivalued F-contractions on metric spaces with a directed graph

2016 ◽  
Vol 32 (1) ◽  
pp. 1-12
Author(s):  
MUJAHID ABBAS ◽  
◽  
MONTHER R. ALFURAIDAN ◽  
TALAT NAZIR ◽  
◽  
...  
Keyword(s):  
Fixed Points ◽  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contraction Mappings

In this paper, we establish the existence of common fixed points of multivalued F-contraction mappings on a metric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature.

WEAKLY CONTRACTIVE MAPPING IN PARTIAL METRIC SPACE

2017 ◽  
Vol 5 (3) ◽  
pp. 377
Author(s):  
Sagita Charolina Sihombing
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Partial Metric Space ◽  
Contractive Mapping ◽  
Partial Metric ◽  
Weakly Contractive Mapping ◽  
Kannan Mapping ◽  
Weakly Contractive

Contractive mapping is one kind of mapping that guarantees a fixed point in a metric space  Many experts has developed this kind of mapping to show the existence of a fixed point such as Kannan mapping and Chatterjea Contractive mapping. In this study, we will show the weakly contractive mapping to show the existence of fixed point in the partial metric space

scholarly journals New Generalizations of Set Valued Interpolative Hardy-Rogers Type Contractions in b-Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Muhammad Usman Ali ◽  
Hassen Aydi ◽  
Monairah Alansari
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Type Contraction

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces and proved that on a complete b-metric space, whose all closed and bounded subsets are compact, the set valued interpolative Hardy-Rogers type contraction mapping has a fixed point. This article presents generalizations of above results by omitting the assumption that all closed and bounded subsets are compact.

scholarly journals Existence of common fixed points via modified mann iteration in convex metric spaces and an invariant approximation result

2010 ◽  
Vol 41 (4) ◽  
pp. 335-348
Author(s):  
G.V.R. Babu ◽  
G.N. Alemayehu
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Convex Metric Space ◽  
Approximation Result ◽  
Mann Iteration ◽  
Invariant Approximation ◽  
Convex Metric Spaces ◽  
Weakly Contractive

We prove the existence of common fixed points for two selfmaps $T$ and $f$ of a convex metric space $X$ via the convergence of modified Mann iteration where $T$ is a nonlinear $f$-weakly contractive selfmap of $X$ and range of $f$ is complete. An invariant approximation result is also proved.

scholarly journals On Wong Type Contractions

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 649
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Admissible Mapping ◽  
Paper Cover ◽  
Type Contraction

In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature.

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