Simulation functions: a survey of recent results

Fixed-disc results via simulation functions

“…For example, let X = R be the set of all real numbers with the usual metric d(x, y) = |x − y| for all x, y ∈ R. The selfmapping T : R → R defined by T x = x 2 − 2 has two fixed points x 1 = −1 and x 2 = 2 . Fixed points of T form the circle C 1 2 , 3 2 = x ∈ R : x − 1 2 = 3 2 . In recent years, the fixed-circle problem and the fixed-disc problem have been studied with this perspective on metric and some generalized metric spaces (see [1, 9, 10, 12-16, 18-20, 23-29] for more details).…”

“…Every Z -contraction mapping is contractive and hence continuous (see [3,8,21] for basic properties and some examples of a Z -contraction). In [8], Khojasteh et al used the notion of a simulation function to unify several existing fixed-point results in the literature.…”

Picard-Jungck Operator for a Pair of Mappings and Simulation Type Functions

“…For examples of simulation functions and -simulation functions see [1][2][3][4][5][6][7][8][9][10][11][12]. Let f and g act naturally maps on a set .…”

“…Corollary 1 can be applied using the simulation function ζ (v, u) = 9 10 u − (2+v)v 1+v for u, v ∈ [0, +∞)…”

On multivalued Suzuki-type θ-contractions and related applications

“…Recently, Khojasteh et al [18] investigated the notion of a simulation function (see also [19][20][21]).…”