Fixed point results of T-Reich contraction, T-Kannan contraction and T-Banach contraction on cone b-metric spaces under generalized c-distance

2021 ◽  
Vol 15 (2) ◽  
pp. 71-83
Author(s):  
Sahar M. Abusalim ◽  
Zaid M. Fadail
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Banach Contraction ◽  
Kannan Contraction

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.

scholarly journals A fixed point theorem of Kannan type that characterizes fuzzy metric completeness

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4811-4819
Author(s):  
Salvador Romaguera
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Kannan Contraction

We obtain a fixed point theorem for complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical Kannan fixed point theorem. We also show that, in fact, our theorem allows to characterize the fuzzy metric completeness, extending in this way the well-known Reich-Subrahmanyam theorem that a metric space is complete if and only if every Kannan contraction on it has a fixed point.

scholarly journals Fixed Point Theorems for Geraghty Type Contractive Mappings and Coupled Fixed Point Results in 0-Complete Ordered Partial Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Esra Yolacan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Partial Metric Spaces ◽  
Banach Contraction

We establish new fixed point theorems in 0-complete ordered partial metric spaces. Also, we give remark on coupled generalized Banach contraction. Some examples illustrate the usability of our results. The theorems presented in this paper are generalizations and improvements of the several well known results in the literature.

scholarly journals Suzuki-Type of Common Fixed Point Theorems in S-Fuzzy Metric Spaces

2021 ◽  
Vol 2 (3) ◽  
pp. 86-91
Author(s):  
M. Jeyaraman ◽  
S. Sowndrarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Banach Contraction ◽  
New Type ◽  
Common Fixed Point Theorems

In this paper, by using of Suzuki-type approach [Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861–1869, 2008.] we prove new type of Suzuki- type fixed point theorem for non-Archimedean S - fuzzy metric spaces which is generalization of Suzuki-Type fixed point results in S - metric spaces.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

scholarly journals On Some Fixed Point Results in E − Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Rachid Mecheraoui ◽  
Zoran D. Mitrović ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Additional Condition ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
New Class ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

scholarly journals Fixed-Point Theorems for θ − ϕ -Contraction in Generalized Asymmetric Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Abdelkarim Kari ◽  
Mohamed Rossafi ◽  
Hamza Saffaj ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In the last few decades, a lot of generalizations of the Banach contraction principle had been introduced. In this paper, we present the notion of θ -contraction and θ − ϕ -contraction in generalized asymmetric metric spaces to study the existence and uniqueness of the fixed point for them. We will also provide some illustrative examples. Our results improve many existing results.

scholarly journals Generalized Ulam-Hyers Stability, Well-Posedness, and Limit Shadowing of Fixed Point Problems forα-β-Contraction Mapping in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Well Posedness ◽  
Banach Contraction ◽  
Limit Shadowing ◽  
New Type ◽  
The Banach Contraction Principle

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-calledα-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

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.

Some deterministic and random fixed point theorems on a graph

2018 ◽  
Vol 26 (4) ◽  
pp. 211-224 ◽  
Author(s):  
Juan J. Nieto ◽  
Abdelghani Ouahab ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Random Fixed Point ◽  
Ordered Metric Spaces ◽  
Banach Contraction

Abstract We present the random version of the classical Banach contraction principle and some of its generalizations to ordered metric spaces or in metric spaces endowed with a graph.

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