Fixed point results for generalized F-contractive and Roger Hardy type F-contractive mappings in G-metric spaces

Advancements in Fixed Point Results of Generalized Metric Spaces: A Survey

“…Interestingly, their results in G-metric spaces cannot be deduced from any existence results in metric spaces in the manner of Jleli and Samet [38] and Samet et al [39]. Consequently [60], denote by ∆ F the family of all functions F : R + −→ R which satisfy the following conditions.…”

“…Singh et al [60] defined generalized F-contraction and Roger Hardy type F-contractive mappings in the framework of G-metric spaces and obtained some fixed point results. Interestingly, their results in G-metric spaces cannot be deduced from any existence results in metric spaces in the manner of Jleli and Samet [38] and Samet et al [39].…”

“…Theorem 103. [60] Let (X, G) be a G-complete metric space and T : X −→ X be a generalized F-contraction.…”

“…Theorem 104. [60] Let (X, G) be a G-complete metric space and T : X −→ X be a Hardy-Rogers type generalized F-contractive mapping, that is, if F ∈ ∆ F and there exists τ > 0, such that τ + F(G(T x, Ty, T 2 y)) ≤ F(αG(x, y, Ty) + β G(x, T x, Ty) + γG(y, Ty, T 2 y) + δ G(y, T 2 x, T 2 y) + ηG(x, T x, T 2 x)), for all x, y ∈ X, G(T x, Ty, T 2 y) > 0 and α, β , γ, δ , η ≥ 0 with α + β + γ + δ + η < 1. Then T has a fixed point in X.…”

Advancements in Hybrid Fixed Point Results and F-Contractive Operators

“…In 2014, Piri and Kumam [14] expanded the work of Wardowski by imposing weaker auxiliary conditions on the self-map of a complete metric space (MS) on the mapping F. Ahmad et al [15] in 2015 defined two classes of functions based on the idea of Fcontraction and proved some FP results in a complete MS. In 2016, Singh et al [16] studied a new form of the Hardy-Roger type in G-metric spaces and improved the main results of [14]. Furthermore, Vujaković et al [17] in 2020 initiated the idea of (φ -F)-weak contraction and proved the corresponding FP results in metric space.…”