Matematik Bölümü / Department of Mathematics
Recent Submissions

Some Results On Hausdorff Metric For Intuitionistic Fuzzy Sets
(Matematikçiler Derneği, 2018)Fuzzy set theory was frstly introduced by L. A. Zadeh in 1965 [1]. In fuzzy sets, every element in the set is accompanied with a function μ(x): X → [0, 1], called membership function. The membership function may have ... 
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 ... 
Some Results on the Fundamental Concepts of Fuzzy Set Theory in Intuitionistic Fuzzy Environment by Using α and β cuts
(University of Nis, 2019)In this paper we have frstly examined the properties of α and β cuts of intuitionistic fuzzy numbers in Rn with the help of wellknown Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the ... 
Approximation by maxmin operators: A general theory and its applications
(Elsevier B.V., 20200901)In this study, we obtain a general approximation theorem for maxmin operators including many significant applications. We also study the error estimation in this approximation by using Hölder continuous functions. The ... 
Analysis of an epidemic model for transmitted disease in two age classes
(Hacettepe Journal of Mathematics and Statistics, 202006)Infectious diseases are a serious problem for public health and spark the interest in interdisciplinary studies. In this paper, we present two mathematical models describing a possible scenario for infectious diseases. The ... 
An observation on the determinant of aSylvesterKac 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. 
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 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 ... 
Formulæ for multiparameter Gaussian qbinomial sums with applications
(Springer Nature, 202006)Some Gaussian qbinomial sum identities from KAO are further generalized, introducing two additional parameters. We prove the claimed results by qcalculus. Finally we present applications to the generalized Fibonomial ... 
Quadratic sums of Gaussian qbinomial coefficients and Fibonomial coefficients
(Springer, 2020)In this paper we evaluate quadratic sums of Gaussian qbinomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of Heine’s transformation, the qPfaff–Saalschutz theorem ... 
A wide class of Combinatorial matrices related with Reciprocal Pascal and Super Catalan matrices
(University of Calgary, 20191225)In this paper, we present a number of combinatorial matrices that are generalizations or variants of the super Catalan matrix and the reciprocal Pascal matrix. We present explicit formulæ for LUdecompositions of all the ... 
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. 
Formulae for two weighted binomial identities with the falling factorials
(Charles Babbage Research Centre, 201804)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 ... 
Error Estimation for Approximate Solutions of Delay Volterra Integral Equations
(Springer Nature Switzerland, 201911)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 ... 
Partial sums of the gaussian qbinomial coefficients, their reciprocals, square and squared reciprocals with applications
(University of Miskolc, 2019)In this paper, we shall derive formulæ for partial sums of the Gaussian qbinomial coefficients, their reciprocals, squares and squared reciprocals. To prove the claimed results, we use qcalculus. As applications of our ... 
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 ... 
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 ... 
A nonlinear generalization of the Filbert matrix and its Lucas analogue
(Taylor and Francis Ltd., 201901)In this paper, we present both a new generalization and an analogue of the Filbert matrix (Formula presented.) by the means of the Fibonacci and Lucas numbers whose indices are in nonlinear form (Formula presented.) for ... 
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 ... 
Evaluation of sums involving products of Gaussian qbinomial coefficients with applications
(De Gruyter, 201904)Sums of products of two Gaussian qbinomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the ...