Kannan's Fixed Point Theorem Research Articles

Answers to questions on Kannan's fixed point theorem in strong $ b $-metric spaces

<abstract><p>Our purpose of this paper is to answer several open questions posed by Doan (AIMS Math., 6 (2021), 7895–7908). First, we present two fixed point theorems, which are positive answers to Doan's questions. Second, we establish a new type of Riech's fixed point theorem to improve a result of Doan. Finally, we offer a straightforward example illustrating that a set-valued mapping satisfying the conditions of our fixed point theorem may has more than one fixed point.</p></abstract>

Various extensions of the Kannan fixed point theorem in C∗-algebra-valued generalized metric spaces

Various extensions of the Kannan fixed point theorem in C∗-algebra-valued generalized metric spaces

Fixed Point Result on Generalized Cone b-Metric Spaces

The purpose of this paper is to prove a fixed point result on contraction mapping in generalized cone b-metric space (in short GCbMS) as a generalization of cone metric space, cone b metric space and rectangular metric space. The conception of generalized metric space is a generalization of that of classical metric space. Several authors have proved fixed point theorems of contractive mappings on generalized metric spaces, which also generalized some corresponding fixed point results in classical metric spaces. In present paper, we prove a result that is extension of the Kannan fixed point theorem proved by Reny George <i>et al</i>. Our result is extend and unify several well known results in the literature available for cone and cone-b metric space.

A new type of Kannan's fixed point theorem in strong $ b $- metric spaces

<abstract> In this paper, we prove some generalizations of Kannan-type fixed point theorems for singlevalued and multivalued mappings defined on a complete strong b- metric space in terms of a Suzuki-type contraction. Our results extend a result of Górnicki ^{[<xref ref-type="bibr" rid="b10">10</xref>]}. Furthermore, after each theorem are exemples and corollaries respectively. </abstract>

Related Suzuki-type fixed point theorems in ordered metric space

In this paper, we use Suzuki-type contraction to prove three fixed point theorems for generalized contractions in an ordered space equipped with two metrics; we obtain some generalizations of the Kannan fixed point theorem. Our results on partially ordered metric spaces generalize and extend some results of Ran and Reurings as well as of Nieto and Rodríguez-López. To illustrate the effectiveness of our main result, we give an application to matrix equations which involves monotone mappings.

Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

Rectangular partial b-metric spaces

In this article concept of rectangular partial b-metric space have been introduced. It is shown that rectangular b-metric can be achieved from rectangular partial b-metric. Moreover equivalence of completeness of both the spaces have been achieved. An analog to Cantor intersection theorem has been established in such spaces. A variant of Banach fixed point theorem and Kannan fixed point theorem are also proved in the language of rectangular partial b-metric spaces.

C^{∗}-algebra-valued rectangular b-metric spaces and some fixed point theorems

The concept of C^{∗}-algebra-valued rectangular b-metric spaces is introduced as a generalization of C^{∗}-algebra-valued b-metric spaces. An analogue of Banach contraction principle and Kannan's fixed point theorem is proved in this space. As applications, existence and uniqueness results for a type of operator equation is given.

Kannan fixed point theorem on generalized metric space with a graph

Kannan fixed point theorem on generalized metric space with a graph

Generalizations of Banach-Kannan-Chatterjea type fixed point theorems on non-normal cone metric spaces with Banach algebras

In this paper, we obtain generalizations of Banach contraction principle, Kannan fixed point theorem and Chatterjea fixed point theorem for mappings satisfying Suzuki type contractive conditions on cone metric spaces over Banach algebras without the assumption of normality. The obtained results generalize and improve the corresponding conclusions in the literature.

The Kannan’s Fixed Point Theorem in a Cone Hexagonal Metric Spaces

In this paper, we prove Kannan's fixed point theorem in a cone hexagonal metric space. Our result extend and improve the recent result of Jleli and Samet (The Kannan's fixed point theorem in a cone rectangular metric space, J. Nonlinear Sci. Appl., 2 (2009), 161 - 167), and many existing results in the literature. Example is given showing that our result are proper extensions of the existing ones.

The Concept of weak (ψ,α,β) for Some Well Known Fixed Point Theorems

Eslamian and Abkar (8) introduced fixed point of the weak- (ψ, α, β) contractive mappings in complete metric space (also see (9)). In this paper we established a generalized concept of the weak-(ψ, α, β) contractive condition depended on another mapping. Thus, we obtained a new generalization of Banach fixed point t heorem, Kannan fixed point theorem and Chatterjea fixed point theorem.

Some Extensions of Kannan Fixed Point Theorem on 2-Metric Spaces

2-metric space is an interesting nonlinear generalization of the classical one of metric space. In this paper we established fixed point theorems in 2-Metric Spaces by using some new extensions of Kannan fixed point theorem obtained by Kannan [1,2]. The result can be considered as an extension and generalization of fixed point theorems on 2-metric spaces and kannan fixed point theorems, given by many well known authors announced in the available literature.

Triple fixed point theorems for mixed monotone Presic-Kannan and Presic-Chatterjea mappings in partially ordered metric spaces

The aim of this paper is to extend the Kannan fixed point theorem from single-valued self mappings T : X → X to mappings F : X3 → X satisfying a Presiˇ c-Kannan type contractive condition: ... or a Presiˇ c-Chatterjea type contractive condition: ... The obtained tripled fixed point theorems extend and unify several related results in literature.

Banach's and Kannan's fixed point results in fuzzy 2-metric spaces

In this paper we establish two common fixed point theorems in fuzzy 2- metric spaces. These theorems are generalizations of the Banach Contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy 2-metric spaces.

EXTENSIONS OF BANACH'S AND KANNAN'S RESULTS IN FUZZY METRIC SPACES

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

The existence of fixed points for new nonlinear multivalued maps and their applications

AbstractIn this paper, we first establish some new fixed point theorems for M T -functions. By using these results, we can obtain some generalizations of Kannan's fixed point theorem and Chatterjea's fixed point theorem for nonlinear multivalued contractive maps in complete metric spaces. Our results generalize and improve some main results in the literature and references therein.Mathematics Subject Classifications47H10; 54H25

Multivalued generalizations of the Kannan fixed point theorem

In this paper we obtain multi-valed mapping generalizations of two recent theorems of Kikkawa and Suzuki [M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings, Fixed Point Theory Appl., (2008), Article ID 649749, 1-8] and the main theorem of Enjouji et all. [Y. Enjouji, M. Nakanishi and T. Suzuki, A Generalization of Kannan?s Fixed Point Theorem, Fixed Point Theory and Applications, Volume 2009, Article ID 192872, 10 pages].

THE KANNANS FIXED POINT THEOREM IN A CONE RECTANGULAR METRIC SPACE

Recently, Azam, Arshad and Beg introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we extend the Kannan's fixed point theorem in such spaces.

ON KANNAN FIXED POINT PRINCIPLE IN GENERALIZED METRIC SPACES

The concept of a generalized metric space, where the triangle inequality has been replaced by a more general one involving four points, has been recently introduced by Branciari. Subsequently, some classical metric fixed point theorems have been transferred to such a space. The aim of this note is to show that Kannan's fixed point theorem in a generalized metric space is a consequence of the Banach contraction principle in a metric space.