Yazar "Cakan, Sumeyye" seçeneğine göre listele

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    Dynamic analysis of a mathematical model with health care capacity for COVID-19 pandemic
    (Pergamon-Elsevier Science Ltd, 2020) Cakan, Sumeyye
    The fact that no there exists yet an absolute treatment or vaccine for COVID-19, which was declared as a pandemic by the World Health Organization (WHO) in 2020, makes very important spread out over time of the epidemic in order to burden less on hospitals and prevent collapsing of the health care system. This case is a consequence of limited resources and is valid for all countries in the world facing with this serious threat. Slowing the speed of spread will probably make that the outbreak last longer, but it will cause lower total death count. In this study, a new SEIR epidemic model formed by taking into account the impact of health care capacity has been examined and local and global stability of the model has been analyzed. In addition, the model has been also supported by some numerical simulations. (C) 2020 Elsevier Ltd. All rights reserved.
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    Mathematical analysis of local and global dynamics of a new epidemic model
    (Tubitak Scientific & Technological Research Council Turkey, 2022) Cakan, Sumeyye
    In this paper, we construct a new SEIR epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number R-0 by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number R-0 is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to R-0. Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle's Invariance Principle associated with Lyapunov functional technique and Li-Muldowney geometric approach, respectively.
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    Normed proper quasilinear spaces
    (Int Scientific Research Publications, 2015) Cakan, Sumeyye; Yilmaz, Yilmaz
    The fundamental deficiency in the theory of quasilinear spaces, introduced by Aseev [S. M. Aseev, Trudy Mat. Inst. Steklov., 167 (1985), 25-52], is the lack of a satisfactory definition of linear dependence-independence and basis notions. Perhaps, this is the most important obstacle in the progress of normed quasilinear spaces. In this work, after giving the notions of quasilinear dependence-independence and basis presented by Banazili[H. K. Banazili, M. Sc. Thesis, Malatya, Turkey (2014)] and Cakan [S. Cakan, Ph.D. Seminar, Malatya, Turkey (2012)], we introduce the concepts of regular and singular dimension of a quasilinear space. Also, we present a new notion namely proper quasilinear spaces and show that these two kind dimensions are equivalent in proper quasilinear spaces. Moreover, we try to explore some properties of finite regular and singular dimensional normed quasilinear spaces. We also obtain some results about the advantages of features of proper quasilinear spaces. (C) 2015 All rights reserved.
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    Riesz Lemma in Normed Quasilinear Spaces and Its an Application
    (Natl Acad Sciences India, 2018) Cakan, Sumeyye; Yilmazl, Yilmaz
    Aseev (Proc Steklov Inst Math 2:23-52, 1986) started a new field in functional analysis by introducing the concept of normed quasilinear spaces which is a generalization of classical normed linear spaces. Then, we introduced the normed proper quasilinear spaces in addition to the notions of regular and singular dimension of a quasilinear space, Cakan and Yilmaz (J Nonlinear Sci Appl 8:816-836, 2015). In this study, we classify the normed proper quasilinear spaces as solid-floored and non solid-floored. Thus, some properties of normed proper quasilinear spaces become more comprehensible. Also we present the counterpart of classical Riesz lemma in normed quasilinear spaces.
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    Topological Quasilinear Spaces
    (Hindawi Publishing Corporation, 2012) Yilmaz, Yilmaz; Cakan, Sumeyye; Aytekin, Sahika
    We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.