Kannan Type Mappings Research Articles

Koreksi pada artikel Hayati dkk.: Teori Titik Tetap untuk Tipe Kannan yang Diperumum dalam Ruang b-Metrik Modular Lengkap

This article is a commentary on research that is conducted by Hayati et al. which was published in Jambura Journal of Mathematics volume 5 number 2 in 2023. It was found that there is an error occurred in the process of proving the fixed point theorems for generalized Kannan type mappings in modular b-metric spaces. This error makes the existence of the fixed point in the theorem is not valid. By adding the convex property to the modular b-metric, the fixed point theorems still holds.

Fixed point theorem for generalized Kannan type mappings

Fixed point theorem for generalized Kannan type mappings

Fixed point theorems for enriched Kannan-type mappings and application

Fixed point theorems for enriched Kannan-type mappings and application

Teori Titik Tetap untuk Tipe Kannan yang Diperumum dalam Ruang b-Metrik Modular Lengkap

Some generalizations of Banach's contraction principle, which is a fixed-point theorem for contraction mapping in metric spaces, have developed rapidly in recent years. Some of the things that support the development of generalization are the emergence of mappings that are more general than contraction mappings and the emergence of spaces that are more general than metric spaces. The generalized Kannan type mappings are one of the mappings that are more general than contraction mappings. Furthermore, some of the more general spaces than metric spaces are b-metric spaces and modular b-metric spaces, which bring the concept of b-metric spaces into modular spaces. The fixed-point theorems for generalized Kannan-type mappings on b-metric spaces have been given. Therefore, this research aims to define generalized Kannan-type mappings on modular b-metric spaces and provide fixed point theorems for the generalized Kannan-type mappings on complete modular b-metric spaces. The definition of generalized Kannan type mapping in modular b-metric spaces is given by generalizing generalized Kannan type mappings in b-metric spaces. Then, the proof of fixed-point theorems for that mapping in modular b-metric spaces is carried out analogously to the proof of the fixed-point theorems for that mapping given in b-metric space. In this article, we obtain the definition of Kannan-type mappings and fixed-point theorems for generalized Kannan-type mappings in modular b-metric spaces and some consequences of the fixed-point theorem. In proving the theorem, a property of altering distance functions in b-metric spaces is generalized into modular b-metric spaces.

Some New Results for a Class of Multivalued Interpolative Kannan-Type Contractions

In this paper, we introduce the notion of multivalued interpolative Kannan-type contractions. We also introduce a more general version of this notion by relaxing the degrees of freedom of the powers arising in the contractive condition. Gaba et al. (2021) recently pointed out a significant error in the paper of Gaba and Karapinar (2019), showing that a particular type of generalized interpolative Kannan-type contraction does not posses a fixed point in general in a complete metric space. Thus, the study of generalized Kannan-type mappings remains an interesting and mathematically challenging area of research. The main aim of this article is to address such existing results for multivalued mappings. We also investigate common fixed points for this type of contractions. Our results extend and unify some existing results in the literature.

Fixed point theorems in preordered sets

Ran and Reurings (Proc Am Math Soc 132(5):1435–1443, 2003) extended the Banach contraction principle to the setting of partially ordered metric spaces and recently Proinov (J Fixed Point Theory Appl 22:21, 2020) extended and unified many earlier fixed point theorems. In this paper we will present analogous results for the significantly wider class of mappings on preordered metric spaces. We give non-trivial examples of Kannan-type mappings.

Fixed Point Theorems for Generalized Kannan-Type Mappings in a New Type of Fuzzy Metric Space

In this paper, first, we introduce a new type of S∗−fuzzy metric space which is a generalization of fuzzy metric spaces. Second, we study the topological properties of S∗−fuzzy metric spaces. Finally, we extend Kannan-type mappings to generalized Kannan-type mappings under ϕ−gauge functions introduced by Fang in S∗−fuzzy metric spaces and prove the existence and uniqueness of fixed point for this kind of mappings. Furthermore, we also obtain the common fixed point theorems for weak compatibility along with E.A. property or CLRg property. Our results extend and improve very recent theorems in the related literature.

Convergence of some iterations for generalized Kannan type mappings in b-metric spaces

Convergence of some iterations for generalized Kannan type mappings in b-metric spaces

Some fixed point theorems for generalized Kannan type mappings in b-metric spaces

In this paper, we prove some fixed point theorems in b-metric spaces using subadditive altering distance function. Some of these results generalize many existing fixed point theorems for Kannan type mappings. The results are justified with suitable examples.

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

The purpose of this article is twofold. Firstly, combining concepts of graph theory and of fixed point theory, we will present a fixed point result for Kannan type mappings, in the framework of recently introduced, graphicalb-metric spaces. Appropriate examples of graphs validate the established theory. Secondly, our focus is to apply the proposed results to some nonlinear problems which are meaningful in engineering and science. Some open problems are proposed.

Some Kannan type fixed point results in rectangular soft metric space and an application of fixed point for thermal science problem

The intention of current study to survey Kannan type mappings for rectangular soft metric space. Some Kannan type results are obtained by using rectangular soft metric and an application for thermal science problem is presented.

On Kannan-Type Contractive Mappings

In this article, we consider Kannan-type contractive self-map T on a metric space (X, d) such thatand establish some new fixed point results without taking the compactness of X and also relaxing the continuity of T. Further, we anticipate a result ensuring the completeness of the space X via fixed point property of this map. Finally, we give an affirmative answer to the open question posed by J. Górnicki [Fixed point theorems for Kannan-type mappings, J. Fixed Point Theory Appl. 2017]. Apart from these, our manuscript consists of several nontrivial examples which signify the motivation of our investigations.

$FG$-coupled fixed point theorems in cone metric spaces

The concept of $FG$- coupled fixed point introduced recently is a generalization of coupled fixed point introduced by Guo and Lakshmikantham. A point $(x,y)\in X\times X$ is said to be a coupled fixed point of the mapping $F: X\times X \rightarrow X$ if $F(x,y)=x$ and $F(y,x)=y$, where $X$ is a non empty set. In this paper, we introduce $FG$- coupled fixed point in cone metric spaces for the mappings $F:X\times Y \rightarrow X$ and $G:Y\times X\rightarrow Y$ and establish some $FG$- coupled fixed point theorems for various mappings such as contraction type mappings, Kannan type mappings and Chatterjea type mappings. All the theorems assure the uniqueness of $FG$- coupled fixed point. Our results generalize several results in literature, mainly the coupled fixed point theorems established by Sabetghadam et al. for various contraction type mappings. An example is provided to substantiate the main theorem.

Fixed point theorems for Kannan type mappings

In this note, we prove some fixed point theorems for Kannan type mappings. We will use the additional conditions as compactness or asymptotic regularity or involutions. Our proofs are inspired by the study of Lipschitzian mappings (Agarwal et al., Fixed point theory for Lipschitzian-type mappings with applications, 2009).

Some common best proximity point theorems in a complete metric space

In this article, we prove the existence and uniqueness of common best proximity point for a pair of non-self mappings satisfying weak P-property in a complete metric space. Moreover, we prove the same for Kannan type mappings and C-contractive mappings using weak P-property by changing non-self mappings to self mappings in a complete metric space. We take much weaker conditions on the mappings to prove our results. An example is presented here to support our main result.

A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces

The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results.

Fixed Point Theorems for Kannan Type Mappings in 2-Menger Spaces

Abstract In this paper we show that the results of Choudhary and Das [2] hold under more general situation

Coupled Kannan-Type Coincidence Point Results in Partially Ordered Fuzzy Metric Spaces

In this paper, we have derived certain coupled coincidence point and fixed point theorems in fuzzy metric spaces for coupled Kannan type mappings which we have defined here. The fuzzy metric space we have considered here is assumed to have a partial order defined on it. We have used Hadzic type t-norm. A common fixed point result follows from an additional assumption of the weak compatibility condition. Some coupled fixed point results in metric spaces are obtained by applications of the results proved in the context of fuzzy metric spaces. Our results are obtained without any assumption of continuity of the mappings. Some corollaries and three illustrative examples are given.

Fixed points of a pair of Kannan type mappings on a closed ball in ordered partial metric spaces

Unique common fixed point results for mappings satisfying locally contractive con- ditions on a closed ball in a complete ordered partial metric space have been established. The notion of dominated mappings of Economics, Finance, Trade and Industry is also been applied to approximate the unique solution to non linear functional equations. Our results improve some well-known, primary and conventional results.

Common Fixed Point Theorems in Generalized Fuzzy Metric Spaces with \(t\)-Norm of Hadzic Type

In this paper, we introduce the notion of generalized fuzzy metric spaces and prove a common fixed point theorem for weakly compatible maps using continuous \(t\)-norm of Hadzic-type (in short \(H\)-type) for a class of generalized Kannan type mappings in the newly defined spaces. At the end, we give example in support of our theorem.