ON THE BEST APPROXIMATION FOR A 2-HYPERPLANE IN 2-INNER PRODUCT SPACES

Majid Abrishami-Moghaddam ,T Sistani

doi:10.12732/ijpam.v98i4.6

Abstract

Recently, some results on best approximation theory in linear 2-normed spaces have been obtained by Y. J. Cho, S. Elumalai, S. S. Kim, Sh. Rezapour and others (see [2], [4], [6], [11], [1], [13]). These papers are based on the research works in normed linear spaces made by I. Singer ([12]), S. S. Dragomir ([3]), and others. The concept which is closely related to 2-normed linear space is 2-inner product space that introduced by Diminnie, Gahler and White in 1973

Highlights

Introduction and PreliminariesRecently, some results on best approximation theory in linear 2-normed spaces have been obtained by Y
These papers are based on the research works in normed linear spaces made by I
The concept which is closely related to 2-normed linear space is 2-inner product space that introduced by Diminnie, Gahler and White in 1973

Summary

ON THE BEST APPROXIMATION FOR

Sistani2 1Department of Mathematics Birjand Branch Islamic Azad University Birjand, IRAN 2Department of Mathematics Kerman Branch Islamic Azad University Kerman, IRAN. AMS Subject Classification: 46C50, 41A50 Key Words: 2-hyperplane, 2-functional, 2-norm attaining, z-representer, z-best approximation, z-proximinal, z-Chebyshev

Introduction and Preliminaries

Then φ is a bounded linear

Main Results

Then y