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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 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 Fixed point theorems for some multi-valued contraction mappings defined in partial Hausdorff metric spaces(2020-10-15) Bozkurt, HacerIn this paper, we give some fixed point theorems for satisfying different contractive conditions on complete partial Hausdorff metric spaces. Also, we prove some fixed point theorems for two operators that do not necessarily commute with each other to have a common fixed point as in metric spaces. We also state an example in support of our conclusions.Öğe Fixed point theorems under some contractive conditions in partial Hausdorff metric spaces(BİSKA Bilisim Company, 2019-09-29) Bozkurt, HacerIn this paper, we investigate some set-valued contraction mappings in partial Hausdorff metric spaces and prove the existence of fixed point of this set-valued mappings in partial Hausdorff metric spaces. We also give an example as support of our results.Öğe Further results in inner product quasilinear spaces(2019-05) Bozkurt, Hacer; Yılmaz, YılmazÖğe New inner product quasilinear spaces on interval numbers(Hindawi, 2016) Bozkurt, Hacer; Yılmaz, YılmazPrimarily we examine the new example of quasilinear spaces, namely, "IRn 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 IRn interval space related to these concepts. Secondly, we present Is,Ic0,Il∞, and Il2 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 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 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 On Orthonormal sets in inner product quasilinear spaces(Tehnical University of Cluj, 2016-05) Yılmaz, Yılmaz; Bozkurt, Hacer; Çakan, SümeyyeÖğe On some maps with P and Q properties in non normal cone metric spaces(Hikari, 2011) Bozkurt, Hacer; Öztürk, Mahpeyker; Başarır, MetinÖğe On some maps with P and Q properties in non normal cone metric spaces(TOBB Ekonomi ve Teknoloji Üniversitesi, 2010) Bozkurt, Hacer; Öztürk, Mahpeyker; Başarır, MetinÖğe Quasilineer uzaylarda bazı yeni sonuçlar(Türk Matematik Derneği, 2017) Bozkurt, Hacer; Yılmaz, YılmazÖğe Sayıların gizemli dünyası kültür ve edebiyatta sayı sembolizmi(Batman Üniversitesi, 2012-04) Bozkurt, Kenan; Bozkurt, HacerSayılar, günlük hayatta nicel değerlendirmelerin temel elemanı olarak yer alan bir işaretler sistemidir. Nicelik yönünden, zaman ve mekân üzerinde konumlandıran bu sistem, günlük hayatta matematiksel kullanımlarının dışına çıkarak kazandıkları değerlerle yeni bir kimliğe bürünür. Bu kimliğin belirleyicileri, her toplumun az çok alışverişte bulunduğu diğer toplumların kültürleri ve sosyal yaşantılarıdır. Temeli bilinmeyen zamanlarda atılmış dini inançlar, tecrübeler, esinlenmeler sayılar etrafında gelişen, nitel denilebilecek değerlerin kaynağı olarak gösterilebilir. Bu bildirimizde kültür ve edebiyatımızda sıkça kullanılan 1, 3ve 40 sayılarının sahip oldukları nitel anlamlar üzerinde durularak bu sayıların kullanımları örneklerle açıklanmaya çalışılmıştır.Öğe Soft quasilinear spaces and soft normed quasilinear spaces(Adıyaman Üniversitesi, 2020-12-30) Bozkurt, HacerIn this study, a recent concepts of soft quasilinear spaces and soft proper quasilinear spaces are presented. Further, soft quasi vectors in soft quasilinear spaces are investigated, and several related properties are examined such as quasilinear dependent and quasilinear independent. Also, the concept of soft quasi norm of soft quasilinear spaces is given. Lastly, soft quasilinear operators on soft normed quasilinear spaces are defined, and some results about the bounded soft quasilinear operators and continuous soft quasilinear operators are obtained.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.Öğe Some new properties of inner product quasilinear spaces(University of Prishtina, 2016-03) Bozkurt, Hacer; Yılmaz, YılmazIn 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, 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 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 properties of orthonormal sets on inner product quasilinear spaces(Matematikçiler Derneği, 2016) Bozkurt, Hacer; Yılmaz, YılmazAseev introduced the notion of quasilinear space and normed quasilinear space [1]. Then he gives some basic definition and theorems related to these spaces. We can see in [1] that, as different from linear spaces, Aseev used the partial order relation when he defined quasilinear spaces and so he can give consistent counterparts of results in linear spaces. This pioneering work has motivated us to introduce the concept of inner product quasilinear spaces and Hilbert Quasilinear spaces which were given in [5]. Our research with these spaces continued to investigate the quasilinear counterparts of fundamental theorems in linear functional analysis. While working in this nonlinear spaces, we have noticed that the new definition is necessary. So, in this study, we give some new concepts related to inner product quasilinear spaces. In this paper, we present some properties of orthogonal and orthonormal sets on inner product quasilinear spaces. We introduce solid floored quasilinear spaces to deal with a better and suitable kind of quasilinear spaces. To define some topics such as Schauder basis, complete orthonormal sequence, orthonormal basis and complete set and some related theorems this classification is crucial. Furthermore, we try to display some geometric differences of inner product quasilinear spaces from the inner product (linear) spaces.
