[PDF] Top 20 Best proximity point theorems for reckoning optimal approximate solutions

... one approximate solution with the least possible error? Best proximity point theory is an outgrowth of attempts in many directions to answer previously posed questions for various families of ... See full document

... an approximate solution is ensured by best approximation theorems, a natural question in this direction is whether it is possible to guarantee the existence of approximate solution that is ... See full document

... whose solutions are the fixed points of the mapping T ...fixed point. Consequently, the equation T x = x could have no solutions, and in this case, it is of a certain interest to determine an element x ... See full document

... some best proximity point results using generalized weak contractions with discontinuous control ...The theorems are established in metric spaces with a partial ...an optimal ... See full document

... a best proximity point theorem for non-self-mappings satisfied proximal cyclic contraction in PM-spaces and this shows the existence of optimal approximate solutions of certain ... See full document

... The best proximity points are usually used to find the optimal approximate solution of the operator equation T x = x, when T has no fixed ...some best proximity point ... See full document

... the best approximation theorems are befitting for furnishing an approximate solution to the equation Tx = x, such results may not afford an approxi- mate solution that is ...hand, best ... See full document

... an approximate solution x in A such that the error d(x, Tx) is mini- mum, where d is the distance ...a best proximity point theorem guarantees the global minimization of d(x, Tx) by the re- ... See full document

... an approximate solution x in A such that the error d(x, Tx) is minimum, where d is the distance ...a best proximity point theorem (for short BPPT) guarantees the global minimiza- tion of d(x, ... See full document

... a best proximity of T if d(x, T x) = d(A, B ). Indeed, a best proximity point theorem details sufficient conditions for the existence of an element x such that the error d(x, T x) is ... See full document

... a point z, then we have a best proximity point for which d(z, Sz) = d(A, ...fixed point to which it reduces in the cases where A ∩B is ...fixed point methodologies are applicable ... See full document

... exhibit the utility of our results. These examples also demonstrate that our results are proper generalizations of the results due to I¸slk et al. [8]. As an application of the concept of ϕ-best proximity ... See full document

... Abstract. In this paper, we introduce Wardowski’s F -contractions in the context of modular function spaces. We also introduce the concept of F ρ -proximal contraction and prove some best proximity ... 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 ... See full document

... fixed point of non-self mappings is one of the interesting subjects in fixed point ...fixed point Tx = ...of best proximity point appears at this point. A point x is ... See full document

... In this paper, we establish coupled best proximity point theorems for multivalued mappings. Our results extend some recent results by Ali et al. (Abstr. Appl. Anal. 2014:181598, 2014) as well ... See full document

... In the past decade, Jachymski [14] entered graphs in metric fixed point theory and generalized the Banach contraction principle in both metric and partially ordered metric spaces. For further works and results in ... See full document

... then the conclusion follows if we show that the set-valued map Hx G − Fx : M M has a fixed point. Since G is onto, then Hx / ∅. Since Fx is admissible and G is quasiadmissible, then Hx is closed acyclic. Now we ... See full document

... Let E : E, · be a normed space, A a nonempty subset of E, and T : A → E a single- valued map. Whenever the equation T x x has no solution in A, it is natural to ask if there exists an approximate solution. Fan 1 ... See full document

... results. Best proximity point theorems with their proofs are stated in Section , and we justify our results by a suitable ...of best proximity points and fixed point ... See full document