Simulation type functions and coincidence points

Abstract

In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [

On non-linear contractions via extended CF-simulation functions

“…We get under way with a brief recollection of elemental notions and some results compiled from [2,12,14,19,21,23,26]. Precisely, all through this paper, N will represent the set of all positive integers and R will mean the set of all real numbers.…”

“…Corollary 4.9. [23] Assume that T, S : X → X are two self-maps on a complete metric space (X, d) such that T(X) ⊆ S(X) and the following conditions hold:…”

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

“…Definition 1. (See [1,2]) We define -class function as a family of continuous mappings : [0, +∞) 2 → R and satisfies the following conditions: (1) (u, v) ≤ u; (2) (u, v) = u ⇔ either u = 0 or v = 0, for all u, v ∈ [0, +∞).…”

“…Employing a family of -class function, authors [1,2] generalized the class of simulation functions introduced by Khojasteh et al ( [3]) as follows: Definition 2. A mapping : [0, +∞) 2 → R has the property , if there exists an ≥ 0 such that (1)…”

“…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 .…”