New Inner Product Quasilinear Spaces on Interval Numbers

Hacer Bozkurt,Yılmaz Yilmaz

doi:10.1155/2016/2619271

Abstract

Primarily we examine the new example of quasilinear spaces, namely, “IRninterval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results onIRninterval space related to these concepts. Secondly, we presentIs,Ic0,Il∞, andIl2quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.

Highlights

In 1986, Aseev generalized the notion linear spaces by introducing firmly quasilinear spaces
This work has motivated a lot of authors to introduce new results on setvalued analysis [2, 3]
In our present paper we examine a new type of a quasilinear space, namely, IRn

Summary

Introduction

In 1986, Aseev generalized the notion linear spaces by introducing firmly quasilinear spaces He used the partial order relation when he defined quasilinear spaces and he can give consistent counterpart of results in linear spaces. One of the most useful examples of a quasilinear space is the set ΩC(E) of all convex compact subsets of a normed space E. The investigation of this class involves a convex interval analysis. Intervals are excellent tools for handling global optimization problems and for supplementing standard techniques. In [4], we give some examples of quasi-inner product properties on ΩC(E) of all convex compact subsets of a normed space E. We obtain some theorems and results related to these new spaces which provide us with improving the elements of the quasilinear functional analysis

Quasilinear Spaces and Hilbert Quasilinear Spaces

Interval Spaces

Interval Sequence Spaces