Browsing Matematik Bölümü / Department of Mathematics by Title
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Modified neural network operators and their convergence properties with summability methods
(Springer, 202007)We study the approximation properties of CardaliaguetEuvrard 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 ktuples asymmetric entries
(Hacettepe University, 20200402)In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two ktuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulæ for their LUdecompositions ... 
New asymmetric generalizations of the Filbert and Lilbert matrices
(Springer Netherlands, 201906)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
(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
(De Gruyter, 202004)In this paper, two new analogues of the Hilbert matrix with fourparameters have been introduced. Explicit formulæ are derived for the LUdecompositions and their inverses, and the inverse matrices of these analogue matrices. 
New reciprocal sums involving finite products of second order recursions
(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
(Charles Babbage Research Centre, 201407)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: qBernstein Operators of MaxProduct Kind
(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 qBernstein polynomials and also the maxproduct algebra. 
Nonlinear BernsteinType operators providing a better error estimation
(University of Miskolc, 2014)In this paper, when approximating a continuos nonnegative 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
(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
(De Gruyter, 201908)We introduce a nonsymmetric matrix defined by qintegers. Explicit formul ae are derived for its LUdecomposition, the inverse matrices L1 and U1 and its inverse. Nonsymmetric variants of the Filbert and Lilbert matrices ... 
A note on the conjecture of Ramirez and Sirvent
(University of Waterloo, 201402)We give a proof of a recent conjecture of Ramirez and Sirvent on the generating function of the incomplete Tribonacci numbers. 
An observation on the determinant of a SylvesterKac type matrix
(sciendo, 20200409)Based on a lessknown result, we prove a recent conjecture concerning the determinant of a certain SylvesterKac type matrix related tosome Lie Algebras. The determinant of an extension of that matrix ispresented. 
On Alternating Weighted Binomıal Sums With Falling Factorıals
(Int Center Scientific Research & Studies, 2017)In this paper, by inspiring from earlier recent works on weighted binomial sums, we introduce and compute new kinds of binomial sums including rising factorial of the summation indices. 
On Binomial Double Sums with Fibonacci and Lucas numbersI
(Charles Babbage Research Centre, 201904)In this paper, we compute various binomial double sums involving the generalized Fibonacci and Lucas numbers as well as their alternating analogous. 
On Binomial Double Sums With Fibonacci And Lucas NumbersII
(Charles Babbage Research Centre, 201904)In this paper, we compute various binomialdoublesums involving the Fibonacci numbers as well as their alternating analogous. It would be interesting that all sums we shall compute are evaluated in nice multiplication ... 
On Fibonomial sums identities with special sign functions: analytically qcalculus approach
(De Gruyter Open Ltd, 20180626)Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. ... 
On solutions of the recursive equations x_{n+1}=x_{n1}^{p}/x_{n}^{p} (p>0) via Fibonaccitype sequences
(201901)Abstract. In this paper, by using the classical Fibonacci sequence and the golden ratio, we ﬁrst give the exact solution of the nonlinear recursive equation xn+1 = xn−1/xn with respect to certain powers of the initial ... 
On sums of squares of Fibonomial coefficients by qcalculus
(World Scientific Publishing Co. Pte Ltd, 201609)We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kili, c and ... 
On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift
(Elsevier Science Bv, 201308)Investors are naturally interested in the supremum and the infimum of stock prices, also in the maximum gain and the maximum loss over a time period. To shed light on these relatively complicated aspects of sample paths, ...