Some new results on inner product quasilinear spaces
CitationBozkurt, H., Yılmaz, Y. (2017). Some new results on inner product quasilinear spaces. International Conference on Mathematics and Mathematics Education (ICMME-2017), 11-13 May 2017, Şanlıurfa.
Aseev in  introduced the theory of quasilinear spaces which is generalization of classical linear spaces. He used the partial order relation when he defined the quasilinear spaces and so he can give consistent counterparts of results in linear spaces. Further, he also described the convergence of sequences and norm in quasilinear space. We see from the definition of quasilinear space which given in , the inverse of some elements of in quasilinear space may not be available. In , these elements are called as singular elements of quasilinear space. At the same time the others which have an inverse are referred to as regular elements. Then, , she noticed that the base of each singular elements of a combination of regular elements of the quasilinear space. Therefore, she defined the concept of the floor of an element in quasilineer space in  which is very convenient for some analysis of quasilinear spaces. This work has motivated us to introduce some results about the floors of inner product quasilinear spaces. In this article, we research on the properties of the floor of an element taken from an inner product quasilinear space. We prove some theorems related to this new concept. Further, we try to explore some new results in quasilinear functional analysis. Also, some examples have been given which provide an important information about the properties of floor of an inner product quasilinear space.