Now showing items 47-66 of 135

    • 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.
    • Generalized Binomial Convolution Of The Mth Powers Of The Consecutive Integers With The General Fibonacci Sequence 

      Kılıç, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T. (De Gruyter Open Ltd, 2016-12)
      In this paper, we consider Gauthier's generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.
    • The generalized Lilbert matrix 

      Kılıç, Emrah; Prodinger, Helmut (Springer, 2016-09)
      We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formul' are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the ...
    • The generalized q-Pilbert matrix 

      Kılıç, Emrah; Prodinger, Helmut (De Gruyter Open Ltd, 2014-10)
      A generalized q-Pilbert matrix from[KILIC, E.-PRODINGER, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89 (2012), 1370-1377] is further generalized, introducing one additional parameter. Explicit formul' are derived for ...
    • The generalized reciprocal super Catalan matrix 

      Kılıç, Emrah; Arikan, Talha (Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2016)
      The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the LU-decomposition and their inverses, as well as the Cholesky ...
    • Generalized double binomial sums families by generating functions 

      Kılıç, Emrah; Belbachir, Hacene (Utilitas Mathematica Publishing Inc., 2017-09)
      We consider various double binomial sums related with certain second, third and fourth order recursions. Moreover a new binomial sums with complex coefficients related with a generalized second order recursion is derived. ...
    • Global Stability Analysis of a General Scalar Difference Equation 

      Merdan, Hüseyin; Gumus, Ozlem Ak; Karahisarli, Gamzegul (L and H Scientific Publishing, LLC, 2018)
      We consider a general ?rst-order scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual ...
    • 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 ...
    • Hopf bifurcation analysis of coupled two-neuron system with discrete and distributed delays 

      Karaoglu, Esra; Yilmaz, Enes; Merdan, Hüseyin (Springer, 2016-07)
      We study the stability and Hopf bifurcation analysis of a coupled two-neuron system involving both discrete and distributed delays. First, we analyze stability of equilibrium point. Choosing delay term as a bifurcation ...
    • 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 ...
    • 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 Bifurcatıon Analysis For A Ratio-Dependent Predator-Prey System Involving Two Delays 

      Karaoglu, E.; Merdan, Hüseyin (Cambridge University Press, 2014-01)
      The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator-prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. ...
    • 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; 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 ...
    • 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 ...