Equivalent Cauchy Sequences in q 1 , q 2 -Quasi Metric-Like Space and Applications to Fixed-Point Theory

Abstract

This paper introduces the concept of $\left(q_1,q_2\right)$ -quasi metric-like space $\left(X,p\right)$ and delves into some topological properties of it. A necessary and sufficient condition related to equivalent Cauchy sequences and Cauchy sequences in $\left(X,p\right)$ have been proved. Furthermore, the results of the fixed point are shown in the setting of $\left(q_1,q_2\right)$ -quasi metric-like space as applications of conditions of equivalent Cauchy sequences. Besides, some instances are inclined to epitomize the examined consequences.