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Öğe Some new results on inner product quasilinear spaces(Taylor & Francis, 2016-06-28) Bozkurt, Hacer; Yılmaz, YılmazIn 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.Öğe Some new results on inner product quasilinear spaces(Matematikçiler Derneği, 2017) Bozkurt, Hacer; Yılmaz, YılmazAseev 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.Öğe Equivalent normed quasilinear spaces(Iksad Publications, 2018) Bozkurt, Hacer; Yılmaz, YılmazAseev introduced the concepts of quasilinear spaces and normed quasilinear spaces, in his article [1]. He used the partial order relation to define quasilinear spaces. He stated properties and results which are quasilinear counterparts of some results in classical linear functional analysis. Also, in [1], he defined the some new concepts which are only meaningful in normed quasilinear spaces. We give, in this presentation, some new results and examples on quasilinear spaces and normed quasilinear spaces. Further, we introduce the concept of equivalent norms on a quasilinear space. By novelty of the new definition, we state on the Hausdorff metric properties for equivalent norms which are extend to the quasilinear context some results of linear functional analysis.Öğe Biquasilinear functionals on quasilinear spaces and some related results(Erzincan Üniversitesi, 2020-03-20) Bozkurt, Hacer; Yılmaz, YılmazIn this paper, we will present the notion of the biquasilinear functional which is a new concept of quasilinear functional analysis. Just like bilinear functional, the notions of a biquasilinear functional and a quadratic form will not need to have the constitution of an inner product quasilinear space. We were able to define these functionals in any quasilinear space. After giving this new notion, we discuss some examples and prove some theorems for considerable exercises to the theory of biquasilinear functionals in Hilbert quasilinear spacesÖğe On inner product quasilinear spaces and hilbert quasilinear spaces(2016) Bozkurt, Hacer; Yılmaz, YılmazIn this paper, we state some properties of inner product quasilinear spaces. Moreover we introduce the concepts of inner product Ω-space, Hilbert Ω-space and investigate some related theorems. Also, we establish some differences of inner product quasilinear spaces from the inner product (linear) spacesÖğe New inner product quasilinear spaces on interval numbers(Matematikçiler Derneği, 2017) Bozkurt, Hacer; Yılmaz, YılmazAseev [2] launched a new branch of functional analysis by introducing the concept of quasilinear spaces which is generalization of classical linear spaces. He proceeds, in a similar way to linear functional analysis on quasilinear spaces by introducing the notions of norm, with quasilinear operators and functional. We know that any inner product space is a normed space and any normed space is a particular class of normed quasilinear space. Hence, this relation and Aseev’s work motivated us to quasilinear counterparts of inner product space in classical analysis in [7]. Generally in [7], we give some consistent quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. In this work, we examine a new type of a quasilinear space, namely, “ ” interval space. We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependenceindependence and basis on quasilinear functional analysis [5], we obtain some results on “ ” interval space related to these concepts. Furthermore, we present the concepts of “ and ” interval sequence spaces as new examples of quasilinear spaces. Moreover, we obtain some theorems and results related to these new spaces which provide us with improving the elements of the quasilinear functional analysis.Öğe Some new theorems in hilbert quasilinear spaces(Van Yüzüncü Yıl Üniversitesi, 2015) Bozkurt, Hacer; Yılmaz, YılmazThis study is concerned with the some new theorems and deÖnitions in Hilbert quasilinear spaces. First, we introduce minimizing vector theorem and some results in Hilbert quasilinear spaces. Next, we provide two main examples: First example is a Hilbert quasilinear space, that does not satisfy the orthogonal decomposition and second example is subset of a Hilbert quasilinear space with the orthogonal decomposition properties. Then, we have from Örst example that any Hilbert quasilinear space may not satisfy the orthogonal decomposition theorem of Hilbert spaces. Finally, we give some results related to above theorems provide an important contributions to the improvement of the quasilinear functional analysis.Öğe Some new properties of inner product quasilinear spaces(Iksad Publications, 2018) Bozkurt, Hacer; Yılmaz, YılmazThe 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.
