New results of tw-normed approach space

Abstract

In this paper, a improved convergence theorem, focal point, tw-Cauchy series, tw-convergent, tw-precision and sequential reduction in tw-approach space are defined and studied. The necessity of achieving the contraction condition in order to get the sequential contraction function is also shown. Moreover, a new structure for the norm in tw-approach space is put, which is called tw-approach-Banach space. Furthermore, tw-approach normed space with uniform condition are given to be a Hausdorff space as well as tw-approach normed space is shown to be the metric space formed by is full if and only if tw-approach space is a complete, so, every finite-dimensional tw-approach normed space is proven to be tw-complete. Some important results and properties in this field are introduced and discussed. is more real in its representation of the relationship between quantity demanded and price, whereas the other model takes into account both demand and Expenses incurred.