Browsing Matematik Bölümü / Department of Mathematics by Title
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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 ... 
Rational points of the curve over
(Cambridge University Press, 201401)Let q be a power of an odd prime. For arbitrary positive integers h, n, m with n dividing m and arbitrary with ? ? 0 we determine the number of rational points of the curve in many cases. 
Robust preconditioners for the highcontrast Stokes equation
(Elsevier Science Bv, 201403)We consider the Stokes equation with highcontrast viscosity coefficients. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by ... 
Ruehr's identities with two additional parameters
(Integers, 201603)We present generalizations of Ruehr’s identities with two additional parameters. We prove the claimed results by two di?erent proof methods, namely combinatorially and mechanically. Further, we derive recurrence relations ... 
Singular approximation in polydiscs by summability process
(Springer, 201609)In this paper, we approximate a continuous function in a polydisc by means of multivariate complex singular operators which preserve the analytic functions. In this singular approximation, we mainly use a regular summability ... 
Smoothness Properties of Modified BernsteinKantorovich Operators
(Taylor and Francis Inc., 201601)In this article, we consider modified BernsteinKantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ... 
Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function
(Matematikçiler Derneği, 201606)In this paper, we reformulate the algorithm in [7] to find an analytical expression for ?cuts of the solution of the second order nonhomogeneous fuzzy initial value problem with fuzzy initial values and fuzzy forcing ... 
Some classes of alternating weighted binomial sums
(201609)In this paper, we consider three classes of generalized alternating weighted binomial sums of the form where f (n, i, k, t) will be chosen as UktiVkn?k(t+2)i, UktiVkn?kti and UtkiV(k+1)tn?(k+2)ti. We use the Binet formula ... 
Some Double binomial sums related to Fibonacci, Pell and generalized orderk Fibonacci numbers
(Rocky Mt Math Consortium, 201310)We consider some double binomial sums related to the Fibonacci and Pell numbers and a multiple binomial sum related to the generalized orderk Fibonaccinumbers. The LagrangeBurmann formula and other wellknown techniques ... 
Some Gaussian binomial sum formulæ with applications
(Indian National Science Academy, 201609)We introduce and compute some Gaussian qbinomial sums formul ae. In order to prove these sums, our approach is to use qanalysis, in particular a formula of Rothe, and computer algebra. We present some applications of our ... 
Some possible fuzzy solutions for second order fuzzy initial value problems involving forcing terms
(Azerbaijan National Academy of Sciences, 2014)In this paper, we state a fuzzy initial value problem of the second order fuzzy differential equations. Here, we investigate problems with fuzzy coefficients, fuzzy initial values, and fuzzy forcing functions where fuzzy ... 
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 ... 
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 ... 
Some Subsequences of the Generalized Fibonacci and Lucas Sequences
(Utilitas Mathematica Publishing Inc., 201507)We derive firstorder nonlinear homogeneous recurrence relations for certain subsequences of generalized Fibonacci and Lucas sequences. We also present a polynomial representation for the terms of Lucas subsequence. 
Some weighted sums of products of Lucas sequences
(Integers, 201311)In this paper, we consider the weighted sums of products of Lucas sequences of the form (Formula Presented) where rn and sn are the terms of Lucas sequences {Un} and {Vn} for some positive integers t and m. By using ... 
Stability and bifurcation analysis of twoneuron network with discrete and distributed delays
(Elsevier B.V., 201603)In this paper, we give a detailed Hopf bifurcation analysis of a recurrent neural network system involving both discrete and distributed delays. Choosing the sum of the discrete delay terms as a bifurcation parameter the ... 
Studying new generalizations of MaxMin matrices with a novel approach
(TÜBİTAK, 2019)We consider new kinds of max and min matrices, [amax(i,j)]i,j?1 and [amin(i,j)]i,j?1, as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence {an} have been ... 
Summability methods in weighted approximation to derivatives of functions
(Bulgarian Academy of Sciences Institute of Mathematics and Informatics, 201504)In this paper, we use summability methods on the approximation to derivatives of functions by a family of linear operators acting on weighted spaces. This point of view enables us to overcome the lack of ordinary convergence ... 
Summability on Mellintype nonlinear integral operators
(Taylor and Francis Ltd., 201903)In this study, approximation properties of the Mellintype nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the ... 
Summability Process by Mastroianni Operators and Their Generalizations
(Birkhauser Verlag AG, 201502)In this paper, we prove a general Korovkintype approximation theorem for the Mastroianni operators using a regular summability process with nonnegative entries. We also obtain some useful estimates via the modulus of ...