Now showing items 61-80 of 135

    • Identities with squares of binomial coefficients: An elementary and explicit approach 

      Kılıç, Emrah; Prodinger, Helmut (Mathematical Institute of the Serbian Academy of Sciences and Arts, 2016)
      In 2014, Slavik presented a recursive method to find closed forms for two kinds of sums involving squares of binomial coefficients. We give an elementary and explicit approach to compute these two kinds of sums. It is based ...
    • 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 ...
    • 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;; 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 ...
    • Intuitionistic Fuzzy Initial Value Problems - An Application 

      Akın, Ömer; Bayeğ, Selami (Hacettepe UniversityHacettpe Üniversitesi, 2019)
      In this paper, by using the properties of ?\alpha? and ?\beta? cuts of intuitionistic fuzzy numbers, we have firstly proposed a method to find the general solution of the second order initial value problem with intuitionistic ...
    • Korovkin theorems on weighted spaces: revisited 

      Atlihan, Ozlem Girgin; Unver, Mehmet; Duman, Oktay (Springer, 2017-12)
      In this note, using the idea of the late Professor Gadjiev (Mat Zametki 20(5):781-786, 1976), we give new, direct and easy proofs of the Korovkin theorems for positive linear operators acting on weighted spaces. Recent ...
    • L-Polynomials of the Curve 

      Ozbudak, Ferruh; Saygı, Zülfükar (Springer Verlag, 2015)
      Let chi be a smooth, geometrically irreducible and projective curve over a finite field F-q of odd characteristic. The L-polynomial L-chi(t) of chi determines the number of rational points of chi not only over F-q but also ...
    • A Mathematical Model Of Hepatitis B Transmission In Turkey 

      Gölgeli, Meltem (Ankara UniversityAnkara Üniversitesi, 2019)
      Hepatitis B infection is one of the serious viral infections that is treating the global health. Turkey has an intermediate endemicity for hepatitis B. In this study, a classical SIR model for hepatitis B virus (HBV) ...
    • 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.), ...
    • The Matrix of Super Patalan Numbers and its Factorizations 

      Kılıç, Emrah; Prodinger, Helmut (University of Nis, 2017)
      Matrices related to Patalan and super-Patalan numbers are factored according to the LU-decomposition. Results are obtained via inspired guessings and later proved using methods from Computer Algebra.
    • 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 ...
    • 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 ...