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Browsing Matematik Bölümü / Department of Mathematics by Submit Date

Browsing Matematik Bölümü / Department of Mathematics by Submit Date

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  • Kılıç, Emrah; Akkuş, İlker (De Gruyter Open Ltd, 2018-06-26)
    Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809-818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. ...
  • Hopkins, Tim; Kılıç, Emrah (Elsevier B. V., 2018-06-01)
    We derive an explicit formula for the inverse of a general, periodic, tridiagonal matrix. Our approach is to derive its LU factorization using backward continued fractions (BCF) which are an essential tool in number theory. ...
  • Kılıç, Emrah; Arıkan, Talha (Chiang Mai University, 2018-05-01)
    In this paper, we derive new double binomial sums families related with generalized second, third and certain higher order linear recurrences. We also present various parametric generalizations of some results of [1, 2]. ...
  • Kılıç, Emrah (TUBITAK, 2018-05-08)
    In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial ...
  • Turan Yalçın, Ceylan; Duman, Oktay (Birkhauser Verlag AG, 2018-10-01)
    Hardy’s well-known Tauberian theorem for number sequences states that if a sequence x= (xk) satisfies lim Cx= L and Δ xk: = xk + 1- xk= O(1 / k) , then lim x= L, where Cx denotes the Cesàro mean (arithmetic mean) of x. In ...
  • Kılıç, Emrah (Springer Berlin Heidelberg, 2018-06-01)
    We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe's formula and a q-version of the celebrated algorithm of Zeilberger. ...
  • Aksoylu, Burak; Unlu, Zuhal (Society for Industrial and Applied Mathematics Publications, 2014-03)
    We study the conditioning of nonlocal integral operators with singular and integrable kernels in fractional Sobolev spaces. These operators are used, for instance, in peridynamics formulation and nonlocal diffusion. In one ...
  • Kılıç, Emrah (Walter De Gruyter Gmbh, 2013-11)
    Recently some generalizations of Sylvester type tridiagonal matrices have been considered with their spectra. We introduce a new kind generalization of Sylvester type tridiagonal matrix by considering its main diagonal entries. ...
  • Duman, Oktay; Ergür, Alperen Ali (Hindawi Publishing, 2013-08)
    We generalize and develop the Korovkin-type approximation theory by using an appropriate abstract space. We show that our approximation is more applicable than the classical one. At the end, we display some applications.
  • Kılıç, Emrah; Prodinger, Helmut (Fibonacci Association, 2013-05)
    A variation of the Filbert matrix from [1] is introduced, which has one additional Fibonacci factor in the numerator. We also introduce its Lucas counterpart by taking Lucas numbers instead of Fibonacci numbers in a similar ...
  • Duman, Oktay; Küçük, Nisa (Bulgarian Academy of Sciences Institute of Mathematics and Informatics, 2015-04)
    In this paper, we use summability methods on the approximation to derivatives of functions by a family of linear operators acting on weighted spaces. This point of view enables us to overcome the lack of ordinary convergence ...
  • Akın, Ömer; Khaniyev, Tahir; Oruc, O.; Türkşen, İ. B. (Pergamon-Elsevier Science Ltd, 2013-01)
    In this paper, we state a fuzzy initial value problem of the second order fuzzy differential equations. Here we investigate problems with fuzzy coefficients, fuzzy initial values and fuzzy forcing functions. We ...
  • Koçak, Neşe; Koçak, Onur; Özbudak, Ferruh; Saygı, Zülfükar (Inderscience Online, 2015)
    In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before ...
  • Kılıç, Emrah; Arıkan, Talha (Integers, 2016-03)
    We present generalizations of Ruehr’s identities with two additional parameters. We prove the claimed results by two di?erent proof methods, namely combinatorially and mechanically. Further, we derive recurrence relations ...
  • Kılıç, Emrah; Ömür, Neşe; Akkus, Ilker; Ulutaş, Yücel T. (Palestine Polytechnic University,, 2015-09)
    We compute certain sums including generalized Fibonacci and Lucas numbers as well as their alternating analogous. We show that these sums could be expressed by the terms of the sequences. Similar directions are given for ...
  • Özpınar, Figen; Koçak, Zeynep Fidan; Akın, Ömer (Matematikçiler Derneği, 2013-01)
    In this paper, some oscillation criteria of certain impulsive partial difference equations with continuous variables are established.
  • Kılıç, Emrah; Ömür, Neşe (Integers, 2013-11)
    In this paper, we consider the weighted sums of products of Lucas sequences of the form (Formula Presented) where rn and sn are the terms of Lucas sequences {Un} and {Vn} for some positive integers t and m. By using ...
  • Kayan, S.; Merdan, Hüseyin (Springer, 2017-07)
    We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf ...
  • Karaoglu, Esra; Yilmaz, Enes; Merdan, Hüseyin (Elsevier B.V., 2016-03)
    In this paper, we give a detailed Hopf bifurcation analysis of a recurrent neural network system involving both discrete and distributed delays. Choosing the sum of the discrete delay terms as a bifurcation parameter the ...
  • Karaoglu, E.; Merdan, Hüseyin (Cambridge University Press, 2014-01)
    The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator-prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. ...