New fixed point results in double controlled metric type spaces with applications

Abstract

<abstract><p>The concept of an $ { \mathcal F} $-contraction was introduced by Wardowski, while Samet et al. introduced the class of $ \alpha $-admissible mappings and the concept of ($ \alpha $-$ \psi $)-contractive mapping on complete metric spaces. In this paper, we study and extend two types of contraction mappings: ($ \alpha $-$ \psi $)-contraction mapping and ($ \alpha $-$ { \mathcal F} $)-contraction mapping, and establish new fixed point results on double controlled metric type spaces. Moreover, we demonstrate some examples and present an application of our result on the existence and uniqueness of the solution for an integral equation.</p></abstract>

Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration

“…This has resulted in the development of various spaces such as b-metric spaces [6], extended b-metric spaces [7], controlled metric spaces [8,9], rectangular metric spaces [10], rectangular b-metric spaces [11,12], and controlled rectangular metric-like spaces [13]. These generalizations offer new perspectives and possibilities in the study of metric spaces, constituting a dynamic and evolving field characterized by continuous research endeavors (for examples, see [10][11][12][14][15][16][17][18][19][20][21][22]). These spaces present novel and intriguing approaches to metric space concepts, showing promise for diverse applications.…”

Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations

“…Abdeljawad et al [5] expanded upon this concept, evolving it into double controlled metric type spaces. Building upon this foundation, Azmi [6] established fixed point results in double controlled metric type spaces by utilizing (α-ψ)-contractive mappings. More recently, Tasneem et al [7] introduced triple controlled metric type spaces and derived their own fixed point results.…”