An alternative and easy approach to fixed point results via simulation functions

Abstract

Abstract:We discuss, extend, improve and enrich results on simulation functions established by several authors. Furthermore, by using Lemma 2.1 of Radenović et al. [Bull. Iran. Math. Soc., 2012, 38, 625], we get much shorter and nicer proofs than the corresponding ones in the existing literature.

Existence of Fixed Points of Four Maps for a New Generalized F-Contraction and an Application

“…Kumam et al [11] showed the existence of fixed points for weak − -contraction mappings in partial metric spaces. Radenović et al [12] investigated the existence of fixed points via simulation functions. Similarly various authors have established (common) fixed point theorems under the notion of a partial metric; see, for example, [13][14][15][16][17][18][19].…”

Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application

“…In 2015, Khojasteh et al [16] presented the notion of Z-contraction involving a new class of mappings-namely, simulation functions, and proved new fixed-point theorems via different methods to others in the literature. For more details, see [17][18][19][20].…”

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 .…”