A bilateral contraction via simulation function

Abstract

In this paper we introduce the notion of a bilateral contraction that combine the ideas ofĆirić type contraction and Caristi type contraction with a help of simulation functions. We investigate the existence of a fixed point of such contractions in the framework of complete metric spaces. We present an example to clarify the statement of the given result.

Common fixed point theorem on Proinov type mappings via simulation function

“…This approach has been considered and improved by several authors; see e.g. [11][12][13][14][15][16][17][18][19][20].…”

Periodic and Fixed Points for Caristi-Type G -Contractions in Extended b -Gauge Spaces

“…In fact, Caristi's theorem is equivalent to metric completeness [3]. For some other contributions to this topic, we refer to [4][5][6][7][8][9][10].…”

Revising the Hardy–Rogers–Suzuki-type Z-contractions

“…As a natural consequence of this fact, some authors proposed new notions to combine and unify this tremendous number of publications in the literature. Here, we mention and use three interesting notions that were proposed for this purpose, namely simulation function (see, e.g., [19][20][21][22][23][24][25][26][27][28][29]), admissible mapping (see, e.g., [9][10][11][12][13][14][15][16][17][18]), and Suzuki-type contraction (see [4,5]).…”

“…We demonstrate here some examples of simulation functions from [10][11][12][13][14][15][16][17][18].…”