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Öğe Analysis of signals with inexact data by using interval-valued functions(Springernature, 2022) Levent, Halise; Yilmaz, YilmazMathematically, a signal is a function of an independent variable t and it contains information about the behavior of the physical quantity. In real life, sometimes a signal value in a time t may not be known exactly. This paper presents a new mathematical method for processing of such a non-deterministic signal by using interval-valued functions which is called as its model interval signal. If the properties of a signal are completely unknown then we cannot perform the processing of these signals such as determining the autocorrelation function of the non-deterministic signal. Especially, in this work, we give an application to estimate the autocorrelation function of a signal with inexact data. For this purpose we use some new mathematical methods so called quasilinear functional analysis. Our studies give approximative result, although there are no definite results for such signals. We think that it's better than not having any information.Öğe Frechet differentiation of nonlinear operators between fuzzy normed spaces(Pergamon-Elsevier Science Ltd, 2009) Yilmaz, YilmazBy the rapid advances in linear theory of fuzzy normed spaces and fuzzy bounded linear operators it is natural idea to set and improve its nonlinear peer. We aimed in this work to realize this idea by introducing fuzzy Frechet derivative based on the fuzzy norm definition in Bag and Samanta [Bag T, Samanta SK. Finite dimensional fuzzy normed linear spaces. J Fuzzy Math 2003; 11(3):687-705]. The definition is divided into two part as strong and weak fuzzy Frechet derivative so that it is compatible with strong and weak fuzzy continuity of operators. Also we restate fuzzy compact operator definition of Lael and Nouroizi [Lael F, Nouroizi K. Fuzzy compact linear operators. Chaos, Solitons & Fractals 2007;34(5):1584-89] as strongly and weakly fuzzy compact by taking into account the compatibility. We prove also that weak Frechet derivative of a nonlinear weakly fuzzy compact operator is also weakly fuzzy compact. (C) 2008 Elsevier Ltd. All rights reserved.Öğe FUNCTION BASES FOR TOPOLOGICAL VECTOR SPACES(Juliusz Schauder Ctr Nonlinear Studies, 2009) Yilmaz, YilmazOur main interest in this work is to characterize certain operator spaces acting on some important vector-valued function spaces such),CA as (V(a))(c0)(a is an element of A), by introducing a new kind basis notion for general Topological vector spaces. Where A is an infinite set, each V(a) is a Banach space and (V(a))(c0)(a is an element of A) is the linear space of all functions x: A -> boolean OR V(a) such that, for each epsilon > 0, the set {a is an element of A : parallel to x(a)parallel to > epsilon} is finite or empty. This is especially important for the vector-valued sequence spaces (V(i))(c0)(i is an element of N) because of its fundamental place in the theory of the operator spaces (see, for example, [12]).Öğe Generalized Kothe-Toeplitz Duals of Some Vector-Valued Sequence Spaces(Hindawi Ltd, 2013) Yilmaz, YilmazWe know from the classical sequence spaces theory that there is a useful relationship between continuous and beta-duals of a scalar-valued FK-space E originated by the AK-property. Our main interest in this work is to expose relationships between the operator space L (E, Y) and E-beta and the generalized beta-duals of some X-valued AK-space E where X and Y are Banach spaces and E-beta = {(A(k)), A(k) epsilon L (X,Y): Sigma(infinity)(k=1) converges in Y, for all x epsilon E}. Further, by these results, we obtain the generalized beta-duals of some vector-valued Orlicz sequence spaces.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 Inner-product quasilinear spaces with applications in signal processing(Tbilisi Centre Math Sci, 2021) Yilmaz, Yilmaz; Levent, HaliseIf certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space Il(2) and we have showed that Il(2) is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.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 Normed proper quasilinear spaces(Int Scientific Research Publications, 2015) Cakan, Sumeyye; Yilmaz, YilmazThe 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.Öğe On some basic properties of differentiation in intuitionistic fuzzy normed spaces(Pergamon-Elsevier Science Ltd, 2010) Yilmaz, YilmazMursaleen and Mohiuddine (2009) [13], introduced Frechet differentiation of nonlinear operators between Intuitionistic Fuzzy normed spaces as a generalization of notions given in Yilmaz (2009) [14]. In this work, we want to advance nonlinear theory of Intuitionistic Fuzzy bounded operators by introducing chain rule and some algebraic properties of Frechet differentiation of operators between Intuitionistic Fuzzy normed spaces. (C) 2010 Elsevier Ltd. All rights reserved.Öğe On Some Topological and Geometric Properties of Some q-Cesaro Sequence Spaces(Mdpi, 2023) Yilmaz, Yilmaz; Akdemir, Ahmet OcakMathematical concepts are aesthetic tools that are useful to create methods or solutions to real-world problems in theory and practice, and that sometimes contain symmetrical and asymmetrical structures due to the nature of the problems. In this study, we investigate whether the sequence spaces X-q(p), 0= p<8, and X8, which are constructed by q-Cesaro matrix, satisfy some of the further properties described with respect to the bounded linear operators on them. More specifically, we answer to the question: Which of these spaces have the Approximation, Dunford-Pettis, Radon-Riesz and Hahn-Banach extension properties?. Furthermore, we try to investigate some geometric properties such as rotundity and smootness of these spaces.Öğe Relative bases in Banach spaces(Pergamon-Elsevier Science Ltd, 2009) Yilmaz, YilmazWe give, in this work, a new basis definition for Banach spaces and investigate some structural properties of certain vector-valued function spaces by using it. By novelty of the new definition, we prove that l(infinity) has a basis in this sense, and so we deduce as a result that it has approximation property. In fact, we obtain a more general result that the linear subspace P (B, X) of l(infinity) (B, X) of all those functions with a precompact range has an XSchauder basis. Hence P (A, X) has approximation property if and only if the Banach space X has. Note that P (B, X) = l(infinity) (B, X) for some finite-dimensional X. Further, we give a representation theorem to operators on certain vector-valued function spaces. (C) 2009 Elsevier Ltd. All rights reserved.Öğe Representations of Operators on Certain Function Spaces and Operator Matrices(Malaysian Mathematical Sciences Soc, 2009) Yilmaz, YilmazContinuous linear operators from l(1) (A, X) and c(0) (A, X) into lambda (A, X), lambda = l(1), l(infinity), or c(0), for a normed space X are investigated. It is shown that such an operator has an operator matrix form whenever A is the set of positive integers.Öğe Schauder bases and approximation property in fuzzy normed spaces(Pergamon-Elsevier Science Ltd, 2010) Yilmaz, YilmazOur aim in this article is to introduce and study the notion of weak and strong Schauder bases in fuzzy normed spaces. Further, we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces. (C) 2009 Elsevier Ltd. All rights reserved.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.Öğe Topological Quasilinear Spaces(Hindawi Publishing Corporation, 2012) Yilmaz, Yilmaz; Cakan, Sumeyye; Aytekin, SahikaWe 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.
