Matematik Bölümü / Department of Mathematics http://hdl.handle.net/20.500.11851/261 2020-02-29T11:27:10Z 2020-02-29T11:27:10Z Error Estimation for Approximate Solutions of Delay Volterra Integral Equations Duman, Oktay http://hdl.handle.net/20.500.11851/3302 2020-01-27T07:06:02Z 2019-11-01T00:00:00Z Error Estimation for Approximate Solutions of Delay Volterra Integral Equations Duman, Oktay Anastassiou, George A.; Rassias, John Michael 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 and convergence analysis are provided. At the end of the paper we display numerical simulations verifying our results. 2019-11-01T00:00:00Z Partial sums of the gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications Kılıç, Emrah Akkuş, İlker http://hdl.handle.net/20.500.11851/2955 2019-12-25T21:05:40Z 2019-01-01T00:00:00Z Partial sums of the gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications Kılıç, Emrah; Akkuş, İlker In this paper, we shall derive formulæ for partial sums of the Gaussian q-binomial coefficients, their reciprocals, squares and squared reciprocals. To prove the claimed results, we use q-calculus. As applications of our results, we give some interesting generalized Fibonomial sums formulæ. 2019-01-01T00:00:00Z A nonsymmetrical matrix and its factorizations Arıkan, Talha Kılıç, Emrah Prodinger, Helmut http://hdl.handle.net/20.500.11851/2956 2019-12-25T21:06:06Z 2019-08-01T00:00:00Z A nonsymmetrical matrix and its factorizations Arıkan, Talha; Kılıç, Emrah; Prodinger, Helmut 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 come out as consequences of our results for special choices of q and parameters. The approach consists of guessing the relevant quantities and proving them later by traditional means. 2019-08-01T00:00:00Z New asymmetric generalizations of the Filbert and Lilbert matrices Kılıç, Emrah Koparal, Sibel Ömür, Neşe http://hdl.handle.net/20.500.11851/2951 2019-12-25T21:06:06Z 2019-06-01T00:00:00Z New asymmetric generalizations of the Filbert and Lilbert matrices Kılıç, Emrah; Koparal, Sibel; Ömür, Neşe 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 their LU-decompositions and inverses. 2019-06-01T00:00:00Z