Abstract
The conceptions of metric spaces and extended b-metric spaces play a major role in proving many theorems of existence solution of such equations as integral or differential equations. The notions of quasi metric spaces and quasi b-metric space are a modification of metric and b-metric spaces. In our article, we introduce the concepts of extended (alpha, xi)-contraction and generalized extended (alpha, xi)-contraction for a self-mapping l(1) in an extended quasi b-metric space. Also, we prove that every extended (alpha, xi)-contraction has a unique fixed point under a set of conditions. As well as, we prove that every generalized extended (alpha, xi)-contraction has a unique solution under some specified conditions. Moreover, an application and an example were added to highlight the importance of our work. Our work modify many exciting results in the literature.