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>