weakly contractive mapping
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2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri

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.


2020 ◽  
Vol 36 (2) ◽  
pp. 303-312
Author(s):  
RAKESH TIWARI ◽  
◽  
MOHAMMAD SAEED KHAN ◽  
SHOBHA RANI ◽  
VLADIMIR RAKOCEVIC ◽  
...  

In this paper, we introduce the notion of generalized weakly contractive mapping of quadratic type and we prove fixed point results for this type of mapping. We justify our result by suitable examples and show that this mapping satisfies properties P and Q. Among other things, as corollaries we recover Banach and Kannan fixed point theorems.


2019 ◽  
Vol 20 (1) ◽  
pp. 33
Author(s):  
S. Sunarsini ◽  
S. Sadjidon ◽  
Annisa Rahmita

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.


2017 ◽  
Vol 5 (3) ◽  
pp. 377
Author(s):  
Sagita Charolina Sihombing

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


2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Uamporn Witthayarat ◽  
Thanyarat Jitpeera ◽  
Poom Kumam

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.


2012 ◽  
Vol 45 (3) ◽  
Author(s):  
B. E. Rhoades ◽  
H. K. Pathak ◽  
S. N. Mishra

AbstractThe purpose of this paper is to present some fixed point theorems for certain weakly contractive mappings, known as weakly (


2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Pongsakorn Sunthrayuth ◽  
Chanan Sudsukh ◽  
Poom Kumam

We introduce a new viscosity approximation method with a weakly contractive mapping of general iterative processes for finding common fixed point of nonexpansive semigroups {T(t):t∈ℝ+} in the framework of Banach spaces. We proved that under some mild conditions these iterative processes converge strongly to the common fixed point of {T(t):t∈ℝ+}, which is the unique solution of some variational inequality. The results obtained in this paper extend and improve on the recent results of Li et al. (2009), Chen and He (2007), and many others as special cases.


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