On Some Novel Fixed Point Results for Generalized -Contractions in�Metric-Like Spaces with Application

Abstract

The focus of our work is on the most recent results in fixed point theory related to contractive mappings. We describe variants of (s, q, φ, F)-contractions that expand, supplement and unify an important work widely discussed in the literature, based on existing classes of interpolative and F-contractions. In particular, a large class of contractions in terms of s, q, φ and F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces. The main result in our paper is that (s, q, φ, F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous. As an application of our results, we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.

General New Results on (ϕ,F)−Contractions in b−Metric-like-Spaces

“…-By taking α(y, z) = v q , we obtain some theorems in [8]. -By taking Γ(u 1 , u 2 , u 3 , u 4 ) = ϕ(u 1 a 1 • u 2 a 2 • u 3 a 3 ) where ϕ is non decreasing function on [0, ∞) such that ∞ ∑ n=1 ϕ n (t) < ∞ for t > 0 and ϕ(t) < t for each t > 0, also a 1 , a 2 , a 3 ≥ 0 with 0 < a 1 + a 2 + a 3 = 1, v = 1, we obtain Definition 3 and, respectively, Theorem 1 in [32], in the (α v q , φ, F ) version.…”

“…We emphasize some of the maingeneralizations that provide great developments to the fixed point theory, such as the concepts of b−metric [2,3] and b−metric-like [4]; many scientists have contributed to this theory with papers and essential results, and furthermore we can list references [5][6][7][8][9][10][11][12][13][14]. In 2012, Samet defined α−admissible mapping [15], and further triangular α−admissible mapping [16].…”

Some New Results for (α, β)-Admissible Mappings in 𝔽-Metric Spaces with Applications to Integral Equations

“…Since then, several fixed point results have been established in the setting of the F-metric space. In 2019, Mitrović et al [11] established fixed point results of Banach, Jungck, Reich, and Berinde, on the F-metric space; see also [12][13][14][15][16][17][18]. In the sequel, we recall some of the basic concepts and outcomes that are required in our main results.…”