Now showing items 71-90 of 135

    • New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries 

      Kılıç, Emrah; Ömür, Neşe; Koparal, Sibel (Hacettepe University, 2020-04-02)
      In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulæ for their LU-decompositions ...
    • New asymmetric generalizations of the Filbert and Lilbert matrices 

      Kılıç, Emrah; Koparal, Sibel; Ömür, Neşe (Springer Netherlands, 2019-06)
      Two new asymmetric generalizations of the Filbert and Lilbert matrices constructed by the products of two Fibonacci and Lucas numbers are considered, with additional parameter settings. Explicit formulæ are derived for ...
    • New binomial double sums with products of Fibonacci and Lucas numbers 

      Kılıç, Emrah; Taşdemir, Funda (Utilitas Mathematica Publisher Inc., 2019)
      In this paper, we consider and compute various interesting families of binomial double sums including products of the Fibonacci and Lucas numbers. These sums have nice representations in terms of again the Fibonacci and ...
    • New Filbert and Lilbert matrices with asymmetric entries 

      Bozdağ, Hacer; Kılıç, Emrah; Akkus, Ilker (De Gruyter, 2020-04)
      In this paper, two new analogues of the Hilbert matrix with four-parameters have been introduced. Explicit formulæ are derived for the LU-decompositions and their inverses, and the inverse matrices of these analogue matrices.
    • New reciprocal sums involving finite products of second order recursions 

      Kılıç, Emrah; Ersanli, Didem (University of Miskolc, 2019)
      In this paper, we present new kinds of reciprocal sums of finite products of general second order linear recurrences. In order to evaluate explicitly them by $q$-calculus, first we convert them into their $q$-notation and ...
    • New Sums Identities In Weighted Catalan Triangle With The Powers Of Generalized Fibonacci And Lucas Numbers 

      Kılıç, Emrah; Yalciner, Aynur (Charles Babbage Research Centre, 2014-07)
      In this paper, we consider a generalized Catalan triangle defined by k(m)/n(2n n - k) for positive integer m. Then we compute the weighted half binomial sums with the certain powers of generalized Fibonacci and Lucas numbers ...
    • Nonlinear Approximation: q-Bernstein Operators of Max-Product Kind 

      Duman, Oktay (Springer Verlag, 2016)
      In this paper, we construct a certain family of nonlinear operators in order to approximate a function by these nonlinear operators. For construction, we use the linear q-Bernstein polynomials and also the max-product algebra.
    • Nonlinear Bernstein-Type operators providing a better error estimation 

      Duman, Oktay (University of Miskolc, 2014)
      In this paper, when approximating a continuos non-negative function on the unit interval, we present an alternative way to the classical Bernstein polynomials. Our new operators become nonlinear, however, for some classes ...
    • Nonlinear variants of the generalized Filbert and Lilbert matrices 

      Kılıç, Emrah; Koparal, Sibel; Ömür, Neşe (TÜBİTAK, 2020)
      In this paper, we present variants of the generalized Filbert and Lilbert matrices by products of the general Fibonacci and Lucas numbers whose indices are in certain nonlinear forms of the indices with certain integer ...
    • A nonsymmetrical matrix and its factorizations 

      Arıkan, Talha; Kılıç, Emrah; Prodinger, Helmut (De Gruyter, 2019-08)
      We introduce a nonsymmetric matrix defined by q-integers. Explicit formul ae are derived for its LU-decomposition, the inverse matrices L-1 and U-1 and its inverse. Nonsymmetric variants of the Filbert and Lilbert matrices ...
    • A note on the conjecture of Ramirez and Sirvent 

      Kılıç, Emrah; Prodinger, Helmut (University of Waterloo, 2014-02)
      We give a proof of a recent conjecture of Ramirez and Sirvent on the generating function of the incomplete Tribonacci numbers.
    • An observation on the determinant of a Sylvester-Kac type matrix 

      Fonseca, Carlos M. da; Kılıç, Emrah (sciendo, 2020-04-09)
      Based on a less-known result, we prove a recent conjecture concern-ing the determinant of a certain Sylvester-Kac type matrix related tosome Lie Algebras. The determinant of an extension of that matrix ispresented.
    • On Alternating Weighted Binomıal Sums With Falling Factorıals 

      Kılıç, Emrah; Omur, Nese; Koparal, Sibel (Int Center Scientific Research & Studies, 2017)
      In this paper, by inspiring from earlier recent works on weighted binomial sums, we introduce and compute new kinds of binomial sums including rising factorial of the summation indices.
    • On Binomial Double Sums with Fibonacci and Lucas numbers-I 

      Kılıç, Emrah; Taşdemir, Funda (Charles Babbage Research Centre, 2019-04)
      In this paper, we compute various binomial double sums involving the generalized Fibonacci and Lucas numbers as well as their alternating analogous.
    • On Binomial Double Sums With Fibonacci And Lucas Numbers-II 

      Kılıç, Emrah; Taşdemir, Funda (Charles Babbage Research Centre, 2019-04)
      In this paper, we compute various binomial-double-sums involving the Fibonacci numbers as well as their alternating analogous. It would be interesting that all sums we shall compute are evaluated in nice multiplication ...
    • 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. ...
    • On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences 

      Öcalan, Özkan; Duman, Oktay (2019-01)
      Abstract. In this paper, by using the classical Fibonacci sequence and the golden ratio, we first give the exact solution of the nonlinear recursive equation xn+1 = xn−1/xn with respect to certain powers of the initial ...
    • On sums of squares of Fibonomial coefficients by q-calculus 

      Kılıç, Emrah; Yalciner, Aynur (World Scientific Publishing Co. Pte Ltd, 2016-09)
      We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kili, c and ...
    • On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift 

      Varda-Acar, Ceren; Zirbel, Craig L.; Székely, Gábor J. (Elsevier Science Bv, 2013-08)
      Investors are naturally interested in the supremum and the infimum of stock prices, also in the maximum gain and the maximum loss over a time period. To shed light on these relatively complicated aspects of sample paths, ...
    • On the exact number of solutions of certain linearized equations 

      Ozbudak, Ferruh; Saygı, Zülfükar (Springer, 2014-11)
      In this note we have revisited some of the results of Trachtenberg (On the cross-correlation functions of maximal linear sequences, Ph.D. thesis, University of Southern California, Los Angeles, 1970), which are directly ...