[PDF] Top 20 A generalization for the best proximity point of Geraghty contractions

... It is clear that some mapping on a complete metric space has no fixed point, that is, d(x, Tx) >  for all x ∈ X. In this case, it is natural to ask the existence and uniqueness of the smallest value of d(x, ... See full document

... (Fixed Point Theory Appl. 2012:231, 2012) observed some best proximity point results for Geraghty contractions by using the ...-Geraghty contractions and show the ... See full document

... the generalization of some results given by Basha ...of best proximity points for proximal β -quasi-contractive mappings for non-self-mappings S : M → N and T : N → ...fixed point of two self ... See full document

... An operator T : A → B is said to be a k-contraction if there exists k ∈ [, ) such that d(Tx, Ty) ≤ kd(x, y) for any x, y ∈ A. Banach’s contraction principle states that when A is a complete subset of X and T is a ... See full document

... a generalization of a metric space by replacing the real numbers with Banach spaces ordered by the given cone [4, ...closest proximity to T x is considerable in optimization ... See full document

... Remark . The best proximity theorem given in this work, more precisely Theorem ., is a quite general result. It is a generalization of Theorem . in [], Theorem  in [], and also Theorem . ... See full document

... Ćirić contractions) and proved that such mappings have a unique fixed point in complete metric ...real generalization of some well-known linear ... See full document

... a best proximity point theorem guarantees the global minimization of d(x, Tx) by the re- quirement that an approximate solution x satisfies the condition d(x, Tx) = d(A, ...called best ... See full document

... the best proximity points of T are the points x ∈ A satisfying d(x, Tx) = d(A, ...on best proximity point theory were studied by giving sufficient conditions assuring the ... See full document

... a generalization of the statistical (probabilistic) metric ...fixed point theory in fuzzy met- ric ...fixed point theorems have also been constructed on the basis of this metric ...fixed point ... See full document

... a best prox- imity point theorem offers sufficient conditions for the existence of an element x, called a best proximity point of the mapping T , satisfying the condition that d(x, Tx) = ... See full document

... studied best proximity point results for Suzuki ...-proximal contractions and estab- lish certain best proximity point theorems for such proximal contractions in ... See full document

... Theorem . Let K be a nonempty, compact and convex subset of a normed space E. Then for any continuous mapping T : K → E , there exists x ∈ K with x – T x = inf y∈K T x – y. Some generalizations and extensions of this ... See full document

... presents best proximity point theorems for new classes of non-self mappings, known as generalized proximal contractions, in the setting of metric ...aforesaid best proximity ... See full document

... Fixed point theory have an important role in many branches of mathematics such as differential and integral equations, optimization and variational ...fixed point equation T x = x, where T : A → B is some ... See full document

... • Exactly speaking, in [], we obtained a theorem connected with Geraghty’s fixed point theorem []. However, in this paper, the difference between the two fixed point theorems is not essential. This means ... See full document

... a best proximity point theorem under the assumption: B is approximatively compact with re- spect to ...various best proximity point results are derived under this assump- tion ... See full document

... In , Caballero et al. introduced a generalized Geraghty-contraction as follows. Definition . [] Let A, B be two nonempty subsets of a metric space (X, d). A mapping T : A → B is said to be a ... See full document

... which implies that (T n x) is a Cauchy sequence. Hence, (T n x) converges to some point t ∈ X, nevertheless, an infinite number of terms of the sequence (T n x) lie in A, as in B and C, as a result, t ∈ A ∩ B ∩ C. ... See full document

... some best proximity point theorems involving Z-proximal contractions; see [, ...g-best proximity point, which is a point x ∈ A such that d(gx, Tx) = d(A, B), ... See full document