A new generalization of the Banach contraction principle

Abstract

We present a new generalization of the Banach contraction principle in the setting of Branciari metric spaces.

New fixed point theorems for theta-phi contraction in complete metric spaces

“…From Definition 1.1, we can know that the Banach contraction is a particular case of θ-contractions, meanwhile there exists a θ-contraction which is not a Banach contraction (see [6]). By using the notion of θ-contraction, Jleli and Samet [6] proved a fixed point theorem which is a generalization of the Banach contraction principle as the following:…”

“…For example, Wardowski [12] introduced the contractive condition by τ + F(d(T x, T y)) F(d(x, y)). Jleli and Samet [6] introduced the contractive condition by θ(d(T x, T y)) [θ(d(x, y))] k (e.g., see [1,3,[8][9][10]12] and the references therein for others).…”

Fixed points for φE-Geraghty contractions

“…It is know that BCP has been extended in many various directions by several authors, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein. The following generalization is due to Geraghty [7].…”

Banach fixed point theorem from the viewpoint of digital topology

“…Based on this approach, the paper [26] firstly studied the almost fixed point property of digital images. To establish digital versions of the Banach fixed point theorem [1] and a generalized Banach contraction principle [19,27], the recent paper [6] studied "Banach fixed point theorem for digital images" and its applications. Thus some important results were obtained.…”

“…Hence the Banach fixed point theorem becomes an essential tool for solution of some problems in mathematics and engineering. Motivated by the Banach fixed point theorem [1], the other tools [5] such as a generalized Banach contraction principle [19,27] were established for studying metric spaces [18,23,24]. Digital topology has a focus on studying digital topological properties of nD digital images [25,26], which have contributed to some areas of computer sciences such as image processing, computer graphics, mathematical morphology and so forth [2,7,20].…”