A note on ‘A best proximity point theorem for Geraghty-contractions’

Abstract

), the authors prove a best proximity point theorem for Geraghty nonself contraction. In this note, not only P-property has been weakened, but also an improved best proximity point theorem will be presented by a short and simple proof. An example which satisfies weak P-property but not P-property has been presented to demonstrate our results. MSC: 47H05; 47H09; 47H10

Best proximity points for cyclic Kannan-Chatterjea- Ćirić type contractions on metric-like spaces

“…In 2011, Sadiq Basha [6] stated the best proximity points theorems for proximal contractions. For other best proximity point results, see [1,7,8,14,15,16,17,18,19,20,22,23,25,26,28]. In this paper, we are concerned with the existence of best proximity points for cyclic Kannan-Chatterjea-Ćirić type contractions in the class of metric-like spaces.…”

Homeomorphism metric space and the fixed point theorems

“…It is interesting that A 0 and B 0 are contained in the boundaries of A and B respectively provided A and B are closed subsets of a normed linear space such that d(A, B) > 0 ( [9,10]). …”

Best Proximity Point Results in Non-Archimedean Modular Metric Space

“…Recently, Zhang et al [16] introduced the following notion and showed that it is weaker than the P-property.…”

“…The reader can refer to [12][13][14][15][16]. Note that best proximity point theorems furnish an approximate solution to the equation Tx = x, when there are not any fixed points for T.…”