New Results of Normed Approach Space Via β-Approach Structure

Researchers have identified and defined β- approach normed space if some conditions are satisfied. In this work, we show that every is a space.However, the converse not necessarily true by giving an example. addition, define β – Banach space, examples given. We also solve problems. discuss finite β-dimensional app-normed β-complete consequent app- space. explain metric but give propositions. If two vector spaces, then get properties equivalent. β-normed spaces norm bounded with condition. functions of contraction, results properties. The sequentially β-contraction explained relation between Hausdorff studied.