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2017 - 20182
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Erişim Hakkı: info:eu-repo/semantics/closedAccess × Konu: Inner Product Quasilinear Space ×

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  • Küçük Resim Yok
    Öğe
    Some new results on inner product quasilinear spaces
    (Matematikçiler Derneği, 2017) Bozkurt, Hacer; Yılmaz, Yılmaz
    Aseev in [1] 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 [1], the inverse of some elements of in quasilinear space may not be available. In [4], 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, [6], 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 [6] 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.
  • Küçük Resim Yok
    Öğe
    Some new properties of inner product quasilinear spaces
    (Iksad Publications, 2018) Bozkurt, Hacer; Yılmaz, Yılmaz
    The theory of quasilinear analysis is one of the fundamental theories in nonlinear analysis which has various applications such as integral and differential equations, approximation theory and bifurcation theory. Aseev generalized the concept of linear spaces, using the partial order relation hence they have defined the quasilinear spaces. He also described the convergence of sequences and norm in quasilinear space. Further, he introduced the concept of Ω-space which is only meaningful in normed quasilinear spaces. In the present presentation, we introduce over symmetric set on a inner product quasilinear spaces. We establish some new results related to this new concept. Further, we obtain new conclusions for orthogonal and orthonormal subspaces of inner product quasilinear spaces. These results generalize recent well known results in the linear inner product spaces. Also, some examples have been given which provide an important contribution to understand the structure of inner product quasilinear spaces.