Recent Submissions

  • 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 ...
  • Evaluation of sums of products of Gaussian q-binomial coefficients with rational weight functions 

    Arıkan, Talha; Kılıç, Emrah; Prodinger, Helmut (TÜBİTAK, 2020)
    Generalizing earlier results, sums over the products of the Gaussian q-binomial coefficients are computed. Some applications of the results for special choices of q are emphasized. The results are obtained by the elementary ...
  • Cubic sums of q-binomial coefficients and the Fibonomial coefficients 

    Chu, Wenchang; Kılıç, Emrah (Rocky Mountain Mathematics Consortium, 2019)
    Triple product sums on the generalized Fibonomial and Lucanomial coefficients are evaluated in closed forms by means of Bailey’s summation formulae for two terminating well-poised 3?2-series.
  • 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 ...
  • Bounds on the expected value of maximum loss of fractional Brownian motion 

    Vardar-Acar, Ceren; Bulut, Hatice (Elsevier B.V., 2015-09)
    It has been theoretically proven through present study that the expected value of maximum loss of fractional Brownian motion up to fixed time t with Hurst parameter [1/2, 1) is bounded above by tH??/2 and below by tH/2. ...
  • Modified neural network operators and their convergence properties with summability methods 

    Türkün, Can; Duman, Oktay (Springer, 2020-07)
    We study the approximation properties of Cardaliaguet-Euvrard type neural network operators. We first modify the operators in order to get the uniform convergence, later we use regular summability matrix methods in the ...
  • Approximation by nonlinear integral operators via summability process 

    Aslan, İsmail; Duman, Oktay (Wiley-VCH Verlag, 2020-03)
    In this paper, we study the approximation properties of nonlinear integral operators of convolution-type by using summability process. In the approximation, we investigate the convergence with respect to both the variation ...
  • Rational points of the curve over 

    Özbudak, Ferruh; Saygı, Zülfükar (Cambridge University Press, 2014-01)
    Let q be a power of an odd prime. For arbitrary positive integers h, n, m with n dividing m and arbitrary with ? ? 0 we determine the number of -rational points of the curve in many cases.
  • Intelligent Mathematics II: Applied Mathematics and Approximation Theory 

    Anastassiou, George A.; Duman, Oktay; TOBB ETU, Faculty of Science and Literature, Department of Mathematics; TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü; https://orcid.org/0000-0001-7779-6877; Duman, Oktay (Springer, 2016)
    This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and ...
  • 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 matrix approach to some second-order difference equations with sign-alternating coefficients 

    Andelic, Milica; Du, Zhibin; da Fonseca, Carlos M.; Kılıç, Emrah (Taylor and Francis Ltd., 2020-02)
    In this paper, we analyse and unify some recent results on the double sequence {yn,k}, for n, k ? 1, defined by the second-order difference equation (Formula presented.) with (Formula presented.) and (Formula presented.), ...
  • Powers Sums of the First and Second Kinds of Chebyshev Polynomials 

    Kılıç, Emrah; Koparal, Sibel; Ömür, Neşe (Springer, 2020-04)
    Odd powers of even-indexed Chebyshev polynomials of the second kind and odd powers of odd-indexed Chebyshev polynomials of the first kind were computed. In this paper, we evaluate all of the rest kinds of power sums of the ...
  • 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.
  • Some Results On Hausdorff Metric For Intuitionistic Fuzzy Sets 

    Akın, Ömer; Bayeğ, Selami (Matematikçiler Derneği, 2018)
    Fuzzy set theory was frstly introduced by L. A. Zadeh in 1965 [1]. In fuzzy sets, every element in the set is accompanied with a function μ(x): X → [0, 1], called membership function. The membership function may have ...
  • An Indicator Operator Algorithm for Solving a Second Order Intuitionistic Fuzzy Initial Value Problem 

    Akın, Ömer; Bayeğ, Selami (Matematikçiler Derneği, 2016)
    L. Zadeh [1] was the first who introduced the concept of fuzzy settheory as an extension of the classical notion of the set theory. He remindedpeople that things are not always black or white; there may besome grey colours ...
  • Some Results on the Fundamental Concepts of Fuzzy Set Theory in Intuitionistic Fuzzy Environment by Using α and β cuts 

    Akın, Ömer; Bayeğ, Selami (University of Nis, 2019)
    In this paper we have frstly examined the properties of α and β cuts of intuitionistic fuzzy numbers in Rn with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the ...
  • Approximation by max-min operators: A general theory and its applications 

    Gökçer, Yeliz Türkan; Duman, Oktay (Elsevier B.V., 2020-09-01)
    In this study, we obtain a general approximation theorem for max-min operators including many significant applications. We also study the error estimation in this approximation by using Hölder continuous functions. The ...
  • Analysis of an epidemic model for transmitted disease in two age classes 

    Gölgeli, Meltem; Atay, F. M. (Hacettepe Journal of Mathematics and Statistics, 2020-06)
    Infectious diseases are a serious problem for public health and spark the interest in interdisciplinary studies. In this paper, we present two mathematical models describing a possible scenario for infectious diseases. The ...
  • 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.
  • 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 ...

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