Common fixed point results via $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi $ b $-metric space

Abstract

<abstract><p>In this paper, we take advantage of implicit relationships to come up with a new concept called "$ \mathcal{A}_{\vartheta} $-$ \alpha $-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi $ b $-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings.</p></abstract>

Unified interpolative of Reich–Rus– Ćirić type contraction in relational metric space with an application

“…The Banach contraction principle, a cornerstone of metric fixed point theory, has found extensive applications across various disciplines, including physics, chemistry, economics, computer science, and biology. Consequently, the exploration and generalization of this principle have become focal points of research within nonlinear analysis [1][2][3][4].…”

Recent Advances in Proximity Point Theory Applied to Fractional Differential Equations

“…First, by modifying the established axioms of metric spaces, researchers have introduced a plethora of novel spaces, collectively referred to as generalized metric spaces. Examples of these include b-metric spaces, partial-metric spaces, metric-like spaces, cone-metric spaces, G-metric spaces, and rectangular-metric spaces, among others see [7][8][9]. Alternatively, mathematicians have substituted the contraction condition with various alternative conditions that broaden the concept of contraction.…”

Controlled S-Metric-Type Spaces and Applications to Fractional Integrals

“…Some of them, such as G-metric space, were defined by Mustafa and Sims [2]; D-metric spaces wre defined by Dhage [3]; and D * -metric spaces were introduced by Sedghi et al [4]. Subsequently, some fixed point theorems have been proved in these spaces [5][6][7]. Additionally, Sedghi et al [8] introduced the notion of a S-metric space and represented some of its properties.…”