Convergence Of Best Proximity Points Research Articles

Strong convergence of best proximity points via projection operators with an application

Strong convergence of best proximity points via projection operators with an application

Existence and convergence of best proximity points for generalized pseudo-contractive and Lipschitzian mappings via an Ishikawa-type iterative scheme

In this article, we prove the existence of the best proximity point for the class of nonself generalized pseudo-contractive and Lipschitzian mappings. Also, we approximate the best proximity point through the proposed Ishikawa’s iteration process for the case of nonself-mappings. Finally, we provide an example to illustrate our main result.

BEST PROXIMITY POINTS OF GENERALIZED p-CYCLIC WEAK φ-CONTRACTIONS

In this manuscript, we extend the notion of generalized cyclic weak φ-contractions to p sets, p ≥ 2. We investigate the convergence of best proximity points of such maps in p-cyclic complete metric spaces. We also give an example to support our main results. Our works generalize and improve the related results in the literature.

Some remarks on convergence of best proximity points and Semi-cyclic contractions

Some remarks on convergence of best proximity points and Semi-cyclic contractions

Existence and convergence of best proximity points in $$\mathrm{{CAT}}_\mathrm{{p}}(0)$$ spaces

In this work, we study existence and convergence of best proximity points of a cyclic contraction mapping in a complete $$\mathrm{{CAT}}_\mathrm{{p}}(0)$$ metric space, with $$p \ge 2$$. The case of coupled best proximity points of a pair of cyclic contraction mappings is also discussed. As an application, we provide sufficient conditions to obtain an extension of the Banach Contraction Principle for coupled fixed points.

On Ω Class of Mappings in a p-Cyclic Complete Metric Space

In this manuscript, we introduce the concept of Ω -class of self mappings on a metric space and a notion of p-cyclic complete metric space for a natural number ( p ≥ 2 ) . We not only give sufficient conditions for the existence of best proximity points for the Ω -class self-mappings that are defined on p-cyclic complete metric space, but also discuss the convergence of best proximity points for those mappings.

Best proximity point theorems for weak cyclic Bianchini contractions

Following the technique introduced in [Eldred, A. A. and Veeramani, P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006], in this paper we will extend Bianchini’s fixed point theorem to best proximity point type theorem. We introduce a new class of contractive conditions, called weak cyclic Bianchini contractions.

On the existence and convergence of best proximity points in Menger probabilistic metric spaces

In this article we will study the existence of best proximity point of some special mappings like cyclic mappings in a Menger probabilistic metric space.

Best proximity pair and fixed point results for noncyclic mappings in convex metric spaces

In this article, we formulate a best proximity pair theorem for noncyclic relatively nonexpansive mappings in convex metrc spaces by using a geometric notion of semi-normal structure. In this way, we generalize a corresponding result in [W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970) 142-149]. We also establish a best proximity pair theorem for pointwise noncyclic contractions in the setting of convex metric spaces. Our result generalizes a result due to Sankara Raju Kosuru and Veeramani [G. Sankara Raju Kosuru and P. Veeramani, A note on existence and convergence of best proximity points for pointwise cyclic contractions, Numer. Funct. Anal. Optim., 82 (2011) 821-830].

Extensions of Edelstein's Theorem on Contractive Mappings

The aim of this article is to provide extensions of Edelstein's theorem for a class of contractive mappings, namely cyclic contractive mappings. We prove the existence and convergence of best proximity points of a cyclic contractive map. We also discuss continuity properties of cyclic contractive maps. Finally, we give a characterization of such maps in the setting of a Hilbert space.

The existence and convergence of best proximity points for generalized proximal contraction mappings

In 2011, Sadiq Basha (Nonlinear Anal. 74:5844-5850, 2011) studied and established best proximity point theorems for proximal contractions of the first and the second kinds which are more general than the fixed point theorems of self-contractions. The purpose of this paper is to extend the notion of proximal contraction mappings of the first and the second kinds. We also establish the existence and convergence of best proximity point theorems for these classes and give an example to validate our main results. MSC:47H10, 47H09.

Best proximity points for asymptotic cyclic contraction mappings

In this paper, we prove the existence and convergence of best proximity points for asymptotic cyclic contractions in metric spaces with the property UC, as well as for asymptotic proximal pointwise contractions in uniformly convex Banach spaces. Moreover, we consider a generalized cyclic contraction mapping and prove the existence of best proximity points for such a mapping in Banach spaces which do not necessarily satisfy the geometric property UC.

Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces

In this paper we consider a cyclic mapping on a partially ordered complete metric space. We prove some fixed point theorems, as well as some theorems on the existence and convergence of best proximity points.

Existence and uniqueness of best proximity points in geodesic metric spaces

A mapping T : A ∪ B → A ∪ B such that T ( A ) ⊆ B and T ( B ) ⊆ A is called a cyclic mapping. A best proximity point x for such a mapping T is a point such that d ( x , T x ) = dist ( A , B ) . In this work we provide different existence and uniqueness results of best proximity points in both Banach and geodesic metric spaces. We improve and extend some results on this recent theory and give an affirmative partial answer to a recently posed question by Eldred and Veeramani in [A.A. Eldred, P. Veeramani Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2) (2006) 1001–1006].

Results on the Existence and Convergence of Best Proximity Points

AbstractWe first consider a cyclic "Equation missing"-contraction map on a reflexive Banach space "Equation missing" and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic "Equation missing"-contraction maps in reflexive Banach spaces in one of their works (2009). In the second part of the paper, we will discuss the existence of best proximity points in the framework of more general metric spaces. We obtain some new results on the existence of best proximity points in hyperconvex metric spaces as well as in ultrametric spaces.

The existence of best proximity points in metric spaces with the property UC

Eldred and Veeramani in [A.A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001–1006. MR2260159] proved a theorem which ensures the existence of a best proximity point of cyclic contractions in the framework of uniformly convex Banach spaces. In this paper we introduce a notion of the property UC and extend the Eldred and Veeramani theorem to metric spaces with the property UC.

Convergence and existence results for best proximity points

We provide a positive answer to a question raised by Eldred and Veeramani [A.A. Eldred, P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006) 1001–1006] about the existence of a best proximity point for a cyclic contraction map in a reflexive Banach space. Moreover, we introduce a new class of maps, called cyclic φ -contractions, which contains the cyclic contraction maps as a subclass. Convergence and existence results of best proximity points for cyclic φ -contraction maps are also obtained.

Existence and convergence of best proximity points

Consider a self map T defined on the union of two subsets A and B of a metric space and satisfying T ( A ) ⊆ B and T ( B ) ⊆ A . We give some contraction type existence results for a best proximity point, that is, a point x such that d ( x , T x ) = dist ( A , B ) . We also give an algorithm to find a best proximity point for the map T in the setting of a uniformly convex Banach space.