Now showing items 1-20 of 135

    • On Fibonomial sums identities with special sign functions: analytically q-calculus approach 

      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. ...
    • An analytical approach: Explicit inverses of periodic tridiagonal matrices 

      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. ...
    • Double binomial sums and double sums related with certain linear recurrences of various order 

      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]. ...
    • Three binomial sums weighted by falling and rising factorials 

      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 ...
    • Hardy-Type Tauberian Conditions on Time Scales 

      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 ...
    • Evaluation of various partial sums of Gaussian q-binomial sums 

      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. ...
    • Generalization of statistical Korovkin theorems 

      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.
    • Variants of the Filbert Matrix 

      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 ...
    • Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces 

      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 ...
    • Sylvester-Tridiagonal Matrix with Alternating main diagonal entries and its Spectra 

      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. ...
    • Summability methods in weighted approximation to derivatives of functions 

      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 ...
    • Some weighted sums of products of Lucas sequences 

      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 ...
    • Various Sums Including the Generalized Fibonacci and Lucas numbers 

      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 ...
    • Oscillation Criteriaof impulsive partial difference Equations 

      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.
    • An Algorithm for the solution of second order Fuzzy Initial Value Problem 

      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 ...
    • Characterisation and enumeration of a class of semi-bent quadratic Boolean functions 

      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 ...
    • Ruehr's identities with two additional parameters 

      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 ...
    • On the Number of Irreducible Polynomials over GF(2) with Some Prescribed Coefficients 

      Afşar, Kübra; Saygı, Zülfükar; Tilenbaev, Ernist; Güner, Erdal (Longdom Publishing, 2017-09)
      In this paper we evaluate the number of monic irreducible polynomials in ??2[??] of even degree ?? whose first four coefficients have prescribed values. This problem first studied in [7] and some approximate results are ...
    • Hopf bifurcations of a ratio-dependent predator-prey model involving two discrete maturation time delays 

      Karaoglu, Esra; Merdan, Hüseyin (Elsevier Ltd, 2014-11)
      In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear ...
    • Hopf bifurcations in Lengyel-Epstein reaction-diffusion model with discrete time delay 

      Merdan, Hüseyin; Kayan, S. (Springer, 2015-02)
      We investigate bifurcations of the Lengyel-Epstein reaction-diffusion model involving time delay under the Neumann boundary conditions. Choosing the delay parameter as a bifurcation parameter, we show that Hopf bifurcation ...