Browsing Matematik Bölümü / Department of Mathematics by Title
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Identities with squares of binomial coefficients: An elementary and explicit approach
(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
(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
(Springer, 2016)This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 2831, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and ... 
Intuitionistic Fuzzy Initial Value Problems  An Application
(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
(Springer, 201712)In this note, using the idea of the late Professor Gadjiev (Mat Zametki 20(5):781786, 1976), we give new, direct and easy proofs of the Korovkin theorems for positive linear operators acting on weighted spaces. Recent ... 
LPolynomials of the Curve
(Springer Verlag, 2015)Let chi be a smooth, geometrically irreducible and projective curve over a finite field Fq of odd characteristic. The Lpolynomial Lchi(t) of chi determines the number of rational points of chi not only over Fq but also ... 
A Mathematical Model Of Hepatitis B Transmission In Turkey
(Ankara UniversityAnkara Üniversitesi, 2019)Hepatitis B infection is one of the serious viral infections that is treating the global health. Turkey has an intermediate endemicity for hepatitis B. In this study, a classical SIR model for hepatitis B virus (HBV) ... 
A matrix approach to some secondorder difference equations with signalternating coefficients
(Taylor and Francis Ltd., 202002)In this paper, we analyse and unify some recent results on the double sequence {yn,k}, for n, k ? 1, defined by the secondorder difference equation (Formula presented.) with (Formula presented.) and (Formula presented.), ... 
The Matrix of Super Patalan Numbers and its Factorizations
(University of Nis, 2017)Matrices related to Patalan and superPatalan numbers are factored according to the LUdecomposition. Results are obtained via inspired guessings and later proved using methods from Computer Algebra. 
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 ...