New Results of Normed Approach Space

Authors

  • Ruaa Kadhim Abbas Department of Mathematics, College of education, University of Al-Qadisiyah, Al-Qadisiya, Iraq
  • Boushra Youssif Hussein Department of Mathematics, College of education, University of Al-Qadisiyah, Al-Qadisiya, Iraq https://orcid.org/0000-0003-4909-0126

DOI:

https://doi.org/10.24996/ijs.2022.63.5.25

Keywords:

Approach space, contraction, approach- metric space, approach vector space

Abstract

     In this work, we introduce  a new convergence formula. We also define cluster point , δ-Cauchy sequence, δ-convergent, δ-completeness , and define sequentially contraction  in approach space. In addition, we prove the contraction condition is necessary and sufficient to get the  function is sequentially contraction  as well as we put a new structure for the norm in the approach space which is called approach –Banach space, we discuss the normed approach space with uniform condition is a Hausdorff space. Also, we prove a normed approach space is complete if and only if the metric generated from approach space is complete as well as prove every finite –dimensional approach normed space is δ-complete. We prove several results and properties in this field.

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Published

2022-05-25

How to Cite

Abbas, R. K. ., & Hussein, B. Y. . (2022). New Results of Normed Approach Space. Iraqi Journal of Science, 63(5), 2103–2113. https://doi.org/10.24996/ijs.2022.63.5.25

Issue

Section

Mathematics