Yazar "Olgun, Ali" seçeneğine göre listele

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    Approximation of functions of two variables by certain linear positive operators
    (Springer India, 2007) Taşdelen, Fatma; Olgun, Ali; Bascanbaz-Tunca, Gülen
    We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.
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    Approximation Properties of Modified Baskakov Gamma Operators
    (Univ Nis, 2021) Arpagus, Seda; Olgun, Ali
    In this paper, we have studied an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem, firste we gave the approximation properties of this operator. Secondly, we computed the rate of convergence of this operator by means of the modulus of continuity and we gave an approximation properties of weighted spaces. Finally, we studied the Voronovskaya type theorem of this operator.
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    A class of linear positive operators in weighted spaces
    (Versita, 2012) Erencin, Aysegul; Ince, H. Gul; Olgun, Ali
    In this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.
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    Generalized Baskakov type operators
    (Walter De Gruyter Gmbh, 2017) Erencin, Aysegul; Olgun, Ali; Tasdelen, Fatma
    In this paper, we introduce a generalization of Baskakov operators based on a function rho. We prove a weighted Korovkin type theorem and compute the rate of convergence via weighted modulus of continuity for these operators. Also we give a Voronovskaya type asymptotic formula.
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    Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions
    (Ovidius Univ Press, 2013) Olgun, Ali; Ince, H. Gul; Tasdelen, Fatma
    In the present paper, we study a Kantorovich type generalization of Meyer-Konig and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0, Lambda], 0 < Lambda < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.
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    Numerical Solution of Conformable Time Fractional Generalized Burgers Equation with Proportional Delay by New Methods
    (2023) Kartal, Abdullah; Anaç, Halil; Olgun, Ali
    By using two new methods, called the conformable fractional q-homotopy analysis transform method and the conformable Shehu homotopy perturbation method, the conformable time-fractional partial differential equations with proportional delay is analysed. The graphs of this equation's numerical solutions are drawn. According to numerical simulations, the proposed methods are effective and reliable.
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    On approximation properties of generalized Lupaş type operators based on Polya distribution with Pochhammer k-symbol
    (Hacettepe University, 2022) Gürel Yılmaz, Övgü; Aktaş, Rabia; Taşdelen, Fatma; Olgun, Ali
    The purpose of this paper is to introduce a Kantorovich variant of Lupaş-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k. © 2022, Hacettepe University. All rights reserved.
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    On approximation properties of generalized Lupas type operators based on Polya distribution with Pochhammer k-symbol
    (Hacettepe Univ, Fac Sci, 2022) Gurel Yilmaz, Ovgu; Aktas, Rabia; Tasdelen, Fatma; Olgun, Ali
    The purpose of this paper is to introduce a Kantorovich variant of Lupas-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k.
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    On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators
    (Ankara Univ, Fac Sci, 2019) Ozhavzali, Muzeyyen; Olgun, Ali
    In the present paper, we introduce certain modification of Szasz-Mirakyan-Kantorovich-type operators in polynomial weighted spaces of continuous functions of two variables. Then we research some approximation properties of these operators. We give some inequalities for the operators by means of the weighted modulus of continuity and also obtain a Voronovskaya-type theorem. Furthermore, in the paper we show that our operators give better degree of approximation of functions belonging to weighted spaces than classical Szasz-Mirakyan operators.
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    On bivariate Meyer-König and Zeller operators
    (Univ Miskolc Inst Math, 2013) Olgun, Ali
    This work relates to bivariate Meyer-Konig and Zeller operators, M-n,M- n is an element of N which are not a tensor product setting. We show the monotonicity of the sequence of operators for n under convexity, moreover we study the property of monotonicity in the sense of Li [9]. Finally, we provide an rth order generalization M-n([r]) of M-n and also study approximation of M-n([r]) .
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    On difference of bivariate linear positive operators
    (Ankara Univ, Fac Sci, 2022) Aremu, Saheed Olaosebikan; Olgun, Ali
    In the present paper we give quantitative type theorems for the differences of different bivariate positive linear operators by using weighted modulus of continuity. Similar estimates are obtained via K-functional and for Chebyshev functionals. Moreover, an example involving Szasz and Szasz-Kantorovich operators is given.
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    Quantitative estimates for bivariate Stancu operators
    (John Wiley and Sons Ltd, 2019) Başcanbaz-Tunca, Gülen; Erençin, Ayşegül; Olgun, Ali
    In this paper, we introduce Voronovskaja-type and Grüss–Voronovskaja- type theorems in quantitative mean with the help of the usual modulus of continuity for bivariate Stancu operators, which are different from a tensor product setting. © 2018 John Wiley & Sons, Ltd.
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    Some $k$-Horn hypergeometric functions and their properties
    (2023) Çatak, Caner; Şahin, Recep; Olgun, Ali; Yağcı, Oğuz
    In the theory of special functions, the $k$-Pochhammer symbol is a generalization of the Pochhammer symbol. With the help of the $k$-Pochhammer symbol, we introduce and study a new generalization of the $k$-Horn hypergeometric functions such as, ${G}_{1}^{k}$, ${G}_{2}^{k}$ and ${G}_{3}^{k}$. Furthermore, several investigations have been carried out for some important recursion formulae for several one variable and two variables $k$-hypergeometric functions. In the light of these studies, we introduce some important recursion formulae for several newly generalized $k$-Horn hypergeometric functions. Finally, we present several relations between some $k$-Horn hypergeometric functions ${G}_{1}^{k}$, ${G}_{2}^{k}$ and ${G}_{3}^{k}$, and $k$-Gauss hypergeometric functions $_{2}{F}_{1}^{k}$.
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    Some properties of the multivariate százs operators
    (Publ House Bulgarian Acad Sci, 2012) Olgun, Ali
    In this work some properties of multivariate Szazs operators are considered. We prove that the Szazs operators preserve some properties of the function of modulus of continuity, Lipschitz condition, and a kind of monotonicity.
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    The new numerical solutions of conformable time fractional generalized Burgers equation with proportional delay
    (2023) Kartal, Abdullah; Anaç, Halil; Olgun, Ali
    The conformable time-fractional partial differential equations with proportional delay are studied using two new methods: the conformable fractional q-homotopy analysis transform method and the conformable Shehu homotopy perturbation method. The numerical solutions to this equation are graphed. Numerical simulations show that the proposed techniques are effective and trustworthy.