Now showing items 26-45 of 122

    • Error Estimation for Approximate Solutions of Delay Volterra Integral Equations 

      Duman, Oktay (Springer Nature Switzerland, 2019-11)
      This work is related to inequalities in the approximation theory. Mainly, we study numerical solutions of delay Volterra integral equations by using a collocation method based on sigmoidal function approximation. Error ...
    • Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method 

      Yerlikaya-Özkurt, F.; Varda-Acar, Ceren; Yolcu-Okura, Y.; Weber, G. -W. (Elsevier Science Bv, 2014-03)
      In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential ...
    • Evaluation of Hessenberg Determinants via Generating Function Approach 

      Kılıç, Emrah; Arikan, Talha (University of Nis, 2017)
      In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover ...
    • Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix 

      Kılıç, Emrah; Arikan, Talha (Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2016)
      The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the ...
    • Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions 

      Kılıç, Emrah; Prodinger, Helmut (World Scientific Publishing Co. Pte Ltd, 2016-03)
      We consider sums of the Gaussian q-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications ...
    • Evaluation of sums involving products of Gaussian q-binomial coefficients with applications 

      Kılıç, Emrah; Prodinger, Helmut (De Gruyter, 2019-04)
      Sums of products of two Gaussian q-binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the ...
    • Evaluation of sums involving products of Gaussian q-binomial coefficients with applications to Fibonomial sums 

      Kılıç, Emrah; Prodinger, Helmut (Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2017)
      Sums of products of two Gaussian q-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting ...
    • 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. ...
    • Evaluation of sums containing triple aerated generalized Fibonomial coefficients 

      Kılıç, Emrah (De Gruyter Open Ltd, 2017-04)
      We evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable q and then to use Rothe's identity ...
    • Explicit maximal and minimal curves over finite fields of odd characteristics 

      Ozbudak, Ferruh; Saygı, Zülfükar (Academic Press Inc Elsevier Science, 2016-11)
      In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special ...
    • Explicit spectrum of a circulant-tridiagonal matrix with applications 

      Kılıç, Emrah; Yalciner, Aynur (American Institute of Physics Inc., 2019-07)
      We consider a circulant-tridiagonal matrix and compute its determinant by using generating function method. Then we explicitly determine its spectrum. Finally we present applications of our results for trigonometric ...
    • Formulae for two weighted binomial identities with the falling factorials 

      Kılıç, Emrah; Ömür, Neşe; Koparal, Sibel (Charles Babbage Research Centre, 2018-04)
      In this paper, we will give closed formulae for weighted and alternating weighted binomial sums with the generalized Fibonacci and Lucas numbers including both falling factorials and powers of indices. Furthermore we will ...
    • Formulas for binomial sums including powers of fibonacci and lucas numbers 

      Kılıç, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel Turker (Politechnica University of Bucharest, 2015)
      Recently Prodinger [2] proved general expansion formulas for sums of powers of Fibonacci and Lucas numbers. In this paper, we will prove general expansion formulas for binomial sums of powers of Fibonacci and Lucas numbers.
    • Formulæ for multi-parameter Gaussian q-binomial sums with applications 

      Kılıç, Emrah; Prodinge, Helmut (Springer Nature, 2020-06)
      Some Gaussian q-binomial sum identities from KAO are further generalized, introducing two additional parameters. We prove the claimed results by q-calculus. Finally we present applications to the generalized Fibonomial ...
    • Formulæ related to the q-Dixon formula with applications to Fibonomial sums 

      Kılıç, Emrah; Prodinger, Helmut (Kluwer Academic Publishers, 2015-06)
      The -analogue of Dixon's identity involves three -binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...
    • Fundamental Properties of Statistical Convergence and Lacunary Statistical Convergence on Time Scales 

      Turan, Ceylan; Duman, Oktay (University of Nis, 2017)
      In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical ...
    • Further results on rational points of the curve y(qn) - y = gamma xqh+1 - alpha over F-qm 

      Cosgun, Ayhan; Saygı, Zülfükar; Ozbudak, Ferruh (Springer, 2016-06)
      Let q be a positive power of a prime number. For arbitrary positive integers h, n, m with n dividing m and arbitrary gamma, alpha is an element of F-qm with gamma not equal 0 the number of F-qm - rational points of the ...
    • A generalization of a conjecture of Melham 

      Kılıç, Emrah; Akkus, Ilker; Prodinger, Helmut (Utilitas Mathematica Publishing Inc., 2014-03)
      A generalization of one of Melham's conjectures is presented. After writing it in terms of Gaussian q binomial coefficients, a solution is found using the elementary technique of partial fraction decomposition.
    • 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.
    • Generalized binary recurrent quasi-cyclic matrices 

      Kılıç, Emrah; Ulutaş, Yücel; Akkuş, İlker; Ömür, Neşe (Eszterhazy Karoly College, 2014-11)
      In this paper, we obtain solutions to infinite family of Pell equations of higher degree based on the more generalized Fibonacci and Lucas sequences as well as their all subsequences of the form {ukn} and {vkn} for odd k > 0.