[PDF] Top 20 Common Best Proximity Points for Cyclic φ-Contraction Maps

... a cyclic ϕ− contraction map. The best proximity point theorems emerge as a natural generalization of fixed point theorems, because a best proximity point reduces to a fixed point ... See full document

... have common fixed points, [, ...have common fixed points with such self- ...of common fixed points in cone met- ric spaces [, ] and in fuzzy metric spaces and under ... See full document

... p-proximal cyclic contraction, which includes the cyclic, Kannan, Chatterjea and Reich contractions as sub-classes, is developed in uniform ...of best proximity points for these ... See full document

... above cyclic representation has also been used in [] to prove the exis- tence of a fixed point for a self-mapping defined on a complete metric space which satisfies a cyclic weak ...of best ... See full document

... Theorem 2.6. Let ϕ : 0, ∞ → 0, ∞ be a strictly increasing map. Also, let A and B be nonempty closed and convex subsets of a reflexive and strictly convex Banach space and T : A ∪ B → A ∪ B a cyclic ... See full document

... Fixed point theory has received much attention in the last decades with a rapidly increas- ing number of related theorems on nonexpansive and on contractive mappings, variational inequalities, optimization etc. Variants ... See full document

... Banach contraction principle is the notation of cyclical maps ...Tx. Best proximity point theorems are relevant in this ...of best proximity point is introduced in ...cyclical ... See full document

... X, Φ is assumed to be endowed with an A-distance or and ...fixed points and best proximity points in restricted p-cyclic self-maps F : X | i∈p A i → X | i∈p A i of X, 8, ... See full document

... of cyclic φ-contractions in metric spaces which contains a class of cyclic contractions as a subclass, introduced by Eldred and Veeramani ...of best proximity points for a ... See full document

... a common solution, called a common fixed point of the mappings S and T ...a common fixed points, it is attempted to find a point x that is closest to both Sx and T x in some ...sense. ... See full document

... The purpose of this paper is to present a new method for the research of best proximity point theorems of nonlinear mappings in metric spaces. In this paper, the P-operator technique, which changes ... See full document

... the best approximate theorems ensure the existence of approximate solution to the equation 𝑇𝑥 = 𝑥, such results may not afford an approximate solution that is ...sense, best proximity point theorems ... See full document

... in cyclic contraction. After that several fixed point and best proximity point results have been proved in cyclic ...a best proximity point for relatively non-expansive ... See full document

... In a similar way, under the assumption (ii), we can obtain the existence of common fixed point of A, B, S and T . Uniqueness of common fixed point follows from the inequality (3.1). Theorem 3.7. Let A, B, S ... See full document

... close proximity to each ...and best proximity point theorems accentuate the preceding viewpoint further to guarantee the existence of an element x such that d(x, Tx) assumes the least possible value ... See full document

... Best proximity point theorems are those results that provide sufficient conditions for the existence of a best proximity point and algorithms for finding best proximity ...that ... See full document

... of best proximity point theorem, so this theorem guarantees the existence of an element x such that d(x, T x) = d(A, B) = inf{d(x, y) : x ∈ A and y ∈ B} then x is called a best proximity point ... See full document

... classical best approximation theorem was introduced by Fan [], that is, if A is a nonempty compact convex subset of a Hausdorff locally convex topological vector space B and T : A → B is a continuous mapping, ... See full document

... a best proximity point ((, ) is a best proximity point of T in ...a cyclic contraction, we cannot invoke the main result of [] to show the existence of the best ... See full document

... proximal contraction for a pair of non-self ...S-proximal contraction if there exist non-negative real numbers α, β, γ, δ with α + 2β + 2γ + δ < 1 such ... See full document