Now showing items 41-60 of 135

    • 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; Prodinger, 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.
    • 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. ...