Discussions on the almost 𝒵-contraction

Abstract

<jats:title>Abstract</jats:title> <jats:p>In this paper, we introduce a new contraction, namely, almost <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2020-0174_eq_003.png" /> <jats:tex-math>{\mathcal{Z}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> contraction with respect to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_math-2020-0174_eq_004.png" /> <jats:tex-math>\zeta \in {\mathcal{Z}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, in the setting of complete metric spaces. We proved that such contraction possesses a fixed point and the given theorem covers several existing results in the literature. We consider an example to illustrate our result.</jats:p>

Solution of Nonlinear Fredholm Integral Equations on Almost Z ⊥ -Contraction

“…It shows that ∁∈ Z (see e.g. [1][2][3][4]). Tus, the required results are obtained as follows from Teorem 3.…”

“…Recently, Kojasteh et al [1] proposed a simulation function that integrates certain known fxed point fndings. Following that, Karapinar and Hima Bindu [2] explored fxed point fndings on the almost Z-contraction. Roldán-López-de-Hierro et al [3] somewhat adjusted their defnition of simulation function and explored the presence and uniqueness of coincidence points of two nonlinear operators using this type of control function.…”

Fixed points for SF-GF-contractive mappings type

“…Corollary 3.1. (See E. Karapinar and V. M. L. Hima Bindu [22]) Let (Σ, δ) be a complete metric space, Q : Σ → Σ be a mapping and…”

A study of k- Contraction and the Triangular a Orbital Admissibility Condition in Quasi-metric Space

“…Recent work of authors (1) and (2) have delved into quasi-metric spaces. The term "generalized contraction" was introduced by (3) , while (4) presented the concept of "almost z-contraction" within metric spaces. In dislocated quasi-metric space, (5) has demonstrated a fixed point theorem for Geraghty quasi-contraction type mappings, employing classical methods for proof.…”