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  • Kılıç, Emrah; Prodinger, Helmut (Mathematical Institute of the Serbian Academy of Sciences and Arts, 2014)
    Four generalizations of the Filbert matrix are considered; with additional asymmetric parameter settings. Explicit formula are derived for the LU-decompositions, their inverses, and the inverse matrix. The approach is ...
  • Kılıç, Emrah; Prodinger, H. (Univ Miskolc Inst Math, 2017)
    Recently Melham [1] gives closed formul ae for certain finite reciprocal sums. In this paper, we present a different approach to compute these sums in closed form. Our approach is straight-forward and simple. First we ...
  • Kılıç, Emrah; Prodinger, Helmut (Politechnica University of Bucharest, 2016)
    We give a systematic approach to compute certain sums of squares Fibonomial coefficients with powers of generalized Fibonacci and Lucas numbers as coefficients; the range of the summation is not the natural one but about ...
  • Kılıç, Emrah; Prodinger, Helmut (De Gruyter Open Ltd, 2016-06)
    We give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms ...
  • Akın, Ömer; Bayeğ, Selami (Kyrgyz Turkish Manas UniversityKırgızistan Türkiye Manas Üniversitesi, 2018)
    In this paper we have rstly dened a metric based on the Hausdor metric in intuitionistic fuzzy environment and studied its properties. Then we have proved that the metric space of intuitionistic fuzzy number valued ...
  • Irmak, Nurettin; Kılıç, Emrah (Udruga Matematicara Osijek, 2016)
    Recently, Witula and Slota have given decompositions of the Cauchy and Ferrers-Jackson polynomials [Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence ...
  • Kılıç, Emrah; Arıkan, Talha (Chiang Mai University, 2018-05-01)
    In this paper, we derive new double binomial sums families related with generalized second, third and certain higher order linear recurrences. We also present various parametric generalizations of some results of [1, 2]. ...
  • Yerlikaya-Özkurt, F.; Varda-Acar, Ceren; Yolcu-Okura, Y.; Weber, G. -W. (Elsevier Science Bv, 2014-03)
    In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential ...
  • Kılıç, Emrah; Arikan, Talha (University of Nis, 2017)
    In this paper, we will present various results on computing of wide classes of Hessenberg matrices whose entries are the terms of any sequence. We present many new results on the subject as well as our results will cover ...
  • Kılıç, Emrah; Arikan, Talha (Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2016)
    The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the ...
  • Kılıç, Emrah; Prodinger, Helmut (Scientific Technical Research Council TurkeyTürkiye bilimsel ve teknolojik araştırma kurumu, 2017)
    Sums of products of two Gaussian q-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting ...
  • Kılıç, Emrah (Springer Berlin Heidelberg, 2018-06-01)
    We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe's formula and a q-version of the celebrated algorithm of Zeilberger. ...
  • Kılıç, Emrah (De Gruyter Open Ltd, 2017-04)
    We evaluate a class of sums of triple aerated Fibonomial coefficients with a generalized Fibonacci number as coefficient. The technique is to rewrite everything in terms of a variable q and then to use Rothe's identity ...
  • Kılıç, Emreah; Yalciner, Aynur (American Institute of Physics Inc., 2019-07)
    We consider a circulant-tridiagonal matrix and compute its determinant by using generating function method. Then we explicitly determine its spectrum. Finally we present applications of our results for trigonometric ...
  • Kılıç, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel Turker (Politechnica University of Bucharest, 2015)
    Recently Prodinger [2] proved general expansion formulas for sums of powers of Fibonacci and Lucas numbers. In this paper, we will prove general expansion formulas for binomial sums of powers of Fibonacci and Lucas numbers.
  • Kılıç, Emrah; Prodinger, Helmut (Kluwer Academic Publishers, 2015-06)
    The -analogue of Dixon's identity involves three -binomial coefficients as summands. We find many variations of it that have beautiful corollories in terms of Fibonomial sums. Proofs involve either several instances of the ...
  • Turan, Ceylan; Duman, Oktay (University of Nis, 2017)
    In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical ...
  • Duman, Oktay; Ergür, Alperen Ali (Hindawi Publishing, 2013-08)
    We generalize and develop the Korovkin-type approximation theory by using an appropriate abstract space. We show that our approximation is more applicable than the classical one. At the end, we display some applications.
  • Kılıç, Emrah; Ulutaş, Yücel; Akkuş, İlker; Ömür, Neşe (Eszterhazy Karoly College, 2014-11)
    In this paper, we obtain solutions to infinite family of Pell equations of higher degree based on the more generalized Fibonacci and Lucas sequences as well as their all subsequences of the form {ukn} and {vkn} for odd k > 0.
  • Kılıç, Emrah; Akkus, Ilker; Omur, Nese; Ulutas, Yucel T. (De Gruyter Open Ltd, 2016-12)
    In this paper, we consider Gauthier's generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.