On best approximation in fuzzy metric spaces

WITHDRAWN: Extended Rectangular Fuzzy B-metric Space

“…Zadeh [36] introduced the concept of a fuzzy set, back in 1965, as an extension of a crisp set where each element of a set has some membership values between [0, 1]. Since then, several mathematical structures have been transformed to fuzzy sets, see ( [1], [9], [13], [19], [30], [32], [34]). Kramosil and Michálek [21] applied this theory to metric spaces and defined fuzzy metric space which could be viewed as a reformulation of statistical metric spaces [25].…”

“…We generalize the Banach contraction principle in the framework of extended rectangular fuzzy b−metric space. 1] is called an extended rectangular fuzzy b−metric on X , if for distinct u, x, y, z ∈ X and t, s, w > 0, following conditions hold:…”

Fuzzy Meir-Keeler’s Contraction and Characterization

“…The phrase of fuzzy metric space (FMS), introduced by Kramosil and Michalek [1], then George and Veeramani [2], modified this idea which has applications in quantum particle physics [3] and in the two-slit experiment [4,5]. Also, the theory of FMS is, in this framework, very disparate from the usual theory of metric best approximation and completion, e.g., see [6] and [7][8][9], respectively. Grabiec [10] developed and extended fixed point theory to probabilistic metric space.…”

Fuzzy b-Metric Spaces: Fixed Point Results for ψ-Contraction Correspondences and Their Application

“…This work has been appreciated by researchers (see [9,10]). This work was extended by several researchers in various ways (compare with [11][12][13][14][15][16][17][18][19][20][21]). Among one of them, in 1969, Nadler proposed Banach's contraction principle for correspondence in Hausdorff metric spaces (see [22]).…”