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Öğe İç çarpım quasilineer uzayları ve bazı genelleştirmeleri(İnönü Üniversitesi, 2016) Bozkurt, Hacer"İç Çarpım Quasilineer Uzayları ve Bazı Genelleştirmeleri" isimli bu tez çalışması beş bölümden oluşmaktadır. Giriş bölümünde quasilineer uzay kavramının gelişim süreci, kullanım alanları ve bir quasilineer uzay örneği verilmiştir. İkinci bölümde daha sonraki bölümlerde kullanılacak olan temel tanım ve teoremler verilmiştir. Üçüncü bölümde quasilineer uzay, normlu quasilineer uzay, Ω−uzayı ve quasilineer operatör kavramları tanıtılmıştır. Ayrıca bu kavramlarla ilgili temel teorem ve sonuçlar da bu bölümde verilmiştir. Dördüncü ve beşinci bölüm çalışmamızın orijinal kısmıdır. Dördüncü bölümde lineer iç çarpım uzaylarının bir genelleştirmesi olan iç çarpım quasilineer uzayları ve Hilbert quasilineer uzaylar tanıtılmıştır. Bu bölüm iç çarpım quasilineer uzaylarıyla ilgili bazı yeni tanım, teorem ve sonuçlardan oluşmaktadır. Quasilineer uzaylarda ortogonal ve ortonormal sistemler ile Hilbert quasilineer uzayların bazı yeni özellikleri bu bölümde incelenmiştir. Ayrıca lineer uzaylardaki bazı teoremlerin quasilineer karşılıkları verilmiştir. Son bölümde ise farklı bir quasilineer uzay örneği olan IRn interval uzayı ve Is, Il∞, Ic, Ic0, Il2 interval dizi uzayları tanıtılarak bu uzaylarla ilgili bazı cebirsel çalışmalar yapılmıştır.Öğe Inner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spaces(Hindawi Ltd, 2022) Yilmaz, Yilmaz; Bozkurt, Hacer; Levent, Halise; Cetinkaya, Uemitt has been shown that the class of fuzzy sets has a quasilinear space structure. In addition, various norms are defined on this class,and it is given that the class of fuzzy sets is a normed quasilinear space with these norms. In this study, we first developed thealgebraic structure of the class of fuzzy setsF(Rn)and gave definitions such as quasilinear independence, dimension, and thealgebraic basis in these spaces. .en, with special norms, namely,?u?q = ( integral(1)(0)(sup(x is an element of[u]alpha)?x?)(q)d alpha)(1/q )where 1 <= q <=infinity, we stated that (F(R-n),?u?(q))is a complete normed space. Furthermore, we introduced an inner product in this space for the case q=2. .e innerproduct must be in the form = integral(1)(0)<[u](alpha),[v](alpha)>(K(Rn))d alpha=integral(1)(0){(Rn)d alpha:a is an element of[u](alpha),b is an element of[v](alpha)}. Foru,v is an element of F(Rn). We alsoproved that the parallelogram law can only be provided in the regular subspace, not in the entire ofF(Rn).Finally, we showed thata special class of fuzzy number sequences is a Hilbert quasilinear space.Öğe New Inner Product Quasilinear Spaces on Interval Numbers(Hindawi Ltd, 2016) Bozkurt, Hacer; Yilmaz, YilmazPrimarily we examine the new example of quasilinear spaces, namely, IR interval 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 on IR interval space related to these concepts. Secondly, we present Is, I-c0, Il(00) and Il(2) quasilinear 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.Öğe On the Algebra of Interval Vectors(2023) Yılmaz, Yılmaz; Levent, Halise; Bozkurt, HacerIn this study, we examine some important subspaces by showing that the set of n-dimensional interval vectors is a quasilinear space. By defining the concept of dimensions in these spaces, we show that the set of $n$-dimensional interval vectors is actually a $(n_{r},n_{s})$-dimensional quasilinear space and any quasilinear space is $left( n_{r},0_{s}right) $-dimensional if and only if it is $n$-dimensional linear space. We also give examples of $(2_{r},0_{s})$ and $(0_{r},2_{s})$-dimensional subspaces. We define the concept of dimension in a quasilinear space with natural number pairs. Further, we define an inner product on some spaces and talk about them as inner product quasilinear spaces. Further, we show that some of them have Hilbert quasilinear space structure.Öğe SOME NEW PROPERTIES OF INNER PRODUCT QUASILINEAR SPACES(Int Center Scientific Research & Studies, 2016) Bozkurt, Hacer; Yilmaz, YilmazIn the present paper, 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.Öğe Some new results on inner product quasilinear spaces(Taylor & Francis As, 2016) Bozkurt, Hacer; Yilmaz, YilmazIn 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.
