scholarly journals Some Fixed-Point Theorems on Generalized Cyclic Mappings in B-Metric-Like Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Shengquan Weng ◽  
Quanxin Zhu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Fixed Point Problems ◽  
Interesting Topic ◽  
Definition Of ◽  
Cyclic Mapping ◽  
Formula Type

In this paper, it is concerned with the cyclic mapping in b-metric-like spaces. The definition of W -type cyclic mappings is proposed, and then, the existence-uniqueness of the fixed points of these cyclic mappings and the corresponding fixed point theorems are studied. In b-metric-like spaces, the promotion of the concept of cyclic mapping is an interesting topic; then, it is worthy to continue to this part of the promotion. On this basis, the concept of φ -type cyclic mapping is proposed in this article, and the existence-uniqueness of fixed-point problems and the corresponding fixed-point theorem are considered and studied. The results of this paper further generalize and extend some previous results.

On common fixed points of a sequence of mappings

2016 ◽  
Vol 09 (03) ◽  
pp. 1650060
Author(s):  
Ravindra K. Bisht
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Type Condition ◽  
Present Theorem

The aim of this paper is to obtain a fixed point theorem for a sequence of mappings satisfying a Lipschitz type condition. As compared to the analogous results, some mappings of the present theorem need not satisfy any noncommutativity conditions and therefore our results generalize a number of well-known fixed point theorems in the existing literature.

Fixed point theorems for a system of transformations in generalized metric spaces

2015 ◽  
Vol 08 (04) ◽  
pp. 1550068 ◽  
Author(s):  
Stefan Czerwik ◽  
Krzysztof Król
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Fixed Point Theorem ◽  
Generalized Metric Spaces ◽  
Generalized Metric

In this paper we present the results on the existence of fixed points of system of mappings in generalized metric spaces generalizing the result of Diaz and Margolis. Also the “local fixed point theorems” of a system of such mappings both in generalized and ordinary metric spaces are stated. Banach fixed point theorem and many others are consequences of our results.

scholarly journals Solving Fixed-Point Problems with Inequality and Equality Constraints via a Non-Interior Point Homotopy Path-Following Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Menglong Su ◽  
Yufeng Shang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Interior Point ◽  
Fixed Point Theorems ◽  
Path Following ◽  
Fixed Point Problems ◽  
Constructive Proof ◽  
Nonconvex Sets ◽  
Smooth Path

In recent years, fixed-point theorems have attracted increasing attention and have been widely investigated by many authors. Moreover, determining a fixed point has become an interesting topic. In this paper, we provide a constructive proof of the general Brouwer fixed-point theorem and then obtain the existence of a smooth path which connects a given point to the fixed point. We also present a non-interior point homotopy algorithm for solving fixed-point problems on a class of nonconvex sets by numerically tricking this homotopy path.

scholarly journals Generalizations of Kannan and Reich Fixed Point Theorems, Using Sequentially Convergent Mappings and Subadditive Altering Distance Functions

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1432
Author(s):  
Alireza Pourmoslemi ◽  
Shayesteh Rezaei ◽  
Tahereh Nazari ◽  
Mehdi Salimi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Distance Functions ◽  
Complete Metric Spaces ◽  
Altering Distance

In this paper, first, using interpolative Kannan type contractions, a new fixed point theorem has been proved. Then, by applying sequentially convergent mappings and using subadditive altering distance functions, we generalize contractions in complete metric spaces. Finally, we investigate some fixed point theorems which are generalizations of Kannan and Reich fixed points.

scholarly journals Alpha- F -Convex Contraction Mappings in b -Metric Space and a Related Fixed Point Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kitila Wirtu Geleta ◽  
Kidane Koyas Tola ◽  
Solomon Gebregiorgis Teweldemedhin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mappings

In this paper, we establish fixed point theorems for α - F -convex contraction mappings in b -metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.

scholarly journals New Extensions of Kannan’s and Reich’s Fixed Point Theorems for Multivalued Maps Using Wardowski’s Technique with Application to Integral Equations

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1090 ◽  
Author(s):  
Pradip Debnath ◽  
Hari Mohan Srivastava
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Integral Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Multivalued Maps ◽  
Proper Extension ◽  
Metric Function ◽  
Symmetric Property

The metric function generalizes the concept of distance between two points and hence includes the symmetric property. The aim of this article is to introduce a new and proper extension of Kannan’s fixed point theorem to the case of multivalued maps using Wardowski’s F-contraction. We show that our result is applicable to a class of mappings where neither the multivalued version of Kannan’s theorem nor that of Wardowski’s can be applied to determine the existence of fixed points. Application of our result to the solution of integral equations has been provided. A multivalued Reich type generalized version of the result is also established.

scholarly journals Fixed point theorem in ultrametric space

2018 ◽  
Vol 12 (2) ◽  
pp. 336-346
Author(s):  
Hamid Mamghaderi ◽  
Hashem Masiha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Ultrametric Space ◽  
Weak Connectivity ◽  
The Relationship

We give a class of generalizations of a number of known fixed point theorems to mappings defined on an ultrametric space and non-Archimedean normed space which are endowed with a graph. We also investigate the relationship between weak connectivity and the existence of fixed points for these mappings.

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.

Fixed Points for Dissipative-Repulsive Systems and Topological Dynamics of Mappings Defined on N-dimensional Cells

2005 ◽  
Vol 5 (3) ◽  
Author(s):  
Marina Pireddu ◽  
Fabio Zanolin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Topological Dynamics ◽  
Continuous Mappings ◽  
Expansion Condition ◽  
Dimensional Cell

AbstractWe prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of ℝ

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.

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