Fixed points for φE-Geraghty contractions

Abstract

In this paper, we introduce the new concept of a generalization of contraction so-called ϕ E -Geraghty contraction and we establish a fixed point theorem for such mappings in complete metric spaces.

New Geraghty type contractions on metric-like spaces

“…On the other hand, very recently Fulga and Proca [9] considered a new type of Geraghty contractions given as follows. Definition 1.5.…”

Fixed points for α-βE-Geraghty contractions on b-metric spaces and applications to matrix equations

“…Very recently, Fulga and Proca [12] introduced the notion of ϕ E -Geraghty contractions and established a fixed point result. Definition 1.10.…”

“…Definition 1.10. [12] Let (X, d) be a metric space. A mapping T : X → X is said to be an ϕ E -Geraghty contraction on (X, d) if there exists ϕ ∈ F such that…”

“…Theorem 1.11. [12] Let (X, d) be a complete metric space and T : X → X be an ϕ E -Geraghty contraction. Then T has a unique fixed point u ∈ X and {T n x} converges to u for all x ∈ X .…”

Some Results on S-Contractions of Type E

“…In the last decades, the renowned metric fixed point results of Banach [1] has been improved, extended, and generalized in several ways, see e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. We first mention that the notion of E-contraction, defined by Fulga and Proca [10,11], is one of the interesting approach to improve the Banach mapping contraction. Another interesting fixed point result was given by Khojasteh et al [19] via the newly defined notion, simulation function.…”