Fixed point theorems for asymptotically regular semigroups equipped with generalized Lipschitzian conditions in metric spaces

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhamad Najibufahmi ◽  
Atok Zulijanto
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Regular Semigroups ◽  
Asymptotically Regular

scholarly journals The asymptotically regularity and sequences in partial cone b-metric spaces with application

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2749-2760 ◽  
Author(s):  
Jerolina Fernandez ◽  
Neeraj Malviya ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Regular Maps ◽  
Partial Cone ◽  
Partial Metric Spaces ◽  
New Space ◽  
Asymptotically Regular

The aim of this paper is to propose a new space called partial cone b-metric space by using both the notions of cone b-metric spaces and partial metric spaces and by defining asymptotically regular maps and sequences. We also prove some fixed point theorems for such maps and sequences. Our results extend and generalize some interesting results of [11] and [21] in partial cone b-metric space. An example is also given to support the validity of our results.

scholarly journals Some fixed point theorems relating to the orbital continuity

2005 ◽  
Vol 36 (1) ◽  
pp. 73-80 ◽  
Author(s):  
C. V. R. Babu ◽  
M. V. R. Kameswari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Asymptotically Regular

In this paper, we prove a fixed point theorem for asymptotically regular mappings on a metric space using orbital continuity of the selfmap. As an application of this result, a fixed point theorem is established in $T$-orbitally complete metric spaces. Our results extend Mukherjee's theorem [4] to $T$-orbitally complete metric spaces, and generalize the theorems of Jotic [5] and Neu{s}i'{c} [6].

scholarly journals Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b -Metric Spaces over Banach Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yan Han ◽  
Shaoyuan Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
New Concepts ◽  
Lipschitz Constants ◽  
Asymptotically Regular ◽  
Type Contraction

In this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b -metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X . Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone b -metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X . Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems.

scholarly journals Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Satish Shukla ◽  
Ishak Altun ◽  
Ravindra Sen
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Regular Mapping ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Asymptotically Regular

The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

Some Fixed Point Theorems in G � Metric Spaces

2019 ◽  
Vol 10 (1) ◽  
pp. 151-158
Author(s):  
Bijay Kumar Singh ◽  
Pradeep Kumar Pathak
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces

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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