Matematik Bölümü / Department of Mathematics
http://hdl.handle.net/20.500.11851/261
2020-02-23T00:11:04ZError Estimation for Approximate Solutions of Delay Volterra Integral Equations
http://hdl.handle.net/20.500.11851/3302
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.
2019-11-01T00:00:00ZPartial sums of the gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications
http://hdl.handle.net/20.500.11851/2955
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.
2019-01-01T00:00:00ZA nonsymmetrical matrix and its factorizations
http://hdl.handle.net/20.500.11851/2956
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.
2019-08-01T00:00:00ZNew asymmetric generalizations of the Filbert and Lilbert matrices
http://hdl.handle.net/20.500.11851/2951
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