Yazar "Ozsarac, Firat" seçeneğine göre listele

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    Approximation properties of Szasz-Mirakyan-Kantorovich type operators
    (Wiley, 2019) Aral, Ali; Limmam, Mohamed Lemine; Ozsarac, Firat
    In this paper, we introduce and study new type Szasz-Mirakyan-Kantorovich operators using a technique different from classical one. This allow to analyze the mentioned operators in terms of exponential test functions instead of the usual polynomial type functions. As a first result, we prove Korovkin type approximation theorems through exponential weighted convergence. The rate of convergence of the operators is obtained for exponential weights.
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    BIVARIATE BERNSTEIN POLYNOMIALS THAT REPRODUCE EXPONENTIAL FUNCTIONS
    (Ankara Univ, Fac Sci, 2021) Bozkurt, Kenan; Ozsarac, Firat; Aral, Ali
    In this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters alpha and beta not only are gained more modeling flexibility to operator but also satisfied to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.
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    Differentiated Bernstein Type Operators
    (PADOVA UNIV PRESS, 2020) Aral, Ali; Acar, Tuncer; Ozsarac, Firat
    The present paper deals with the derivatives of Bernstein type operators preserving some exponential functions. We investigate the uniform convergence of the differentiated operators. The rate of convergence by means of a modulus of continuity is studied, an upper estimate theorem for the difference of new constructed differentiated Bernstein type operators is presented.
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    On semi-exponential Gauss-Weierstrass operators
    (Springer Basel Ag, 2022) Gupta, Vijay; Aral, Ali; Ozsarac, Firat
    The paper deals with the semi-exponential type Gauss-Weierstrass operators. The central moments of these operators are constant functions. We estimate some direct results. We also provide a modification of such operators so as the preserve two exponential functions, we estimate weighted approximation, quantitative asymptotic formula for the modified form of operators. Later, a comparison is stated, that shows that in a certain sense and for certain family of illustrative functions the modified form of the semi-exponential Gauss-Weierstrass operators approximates better than the classical ones. Finally, we give some numerical results, which help us better understand the theoretical results obtained in the previous sections.
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    On the generalized Mellin integral operators
    (De Gruyter Poland Sp Z O O, 2024) Topuz, Cem; Ozsarac, Firat; Aral, Ali
    In this study, we give a modification of Mellin convolution-type operators. In this way, we obtain the rate of convergence with the modulus of the continuity of the m m th-order Mellin derivative of function f f , but without the derivative of the operator. Then, we express the Taylor formula including Mellin derivatives with integral remainder. Later, a Voronovskaya-type theorem is proved. In the last part, we state order of approximation of the modified operators, and the obtained results are restated for the Mellin-Gauss-Weierstrass operator.
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    On the Modification of Mellin Convolution Operator and Its Associated Information Potential
    (Taylor & Francis Inc, 2023) Ozsarac, Firat; Acu, Ana Maria; Aral, Ali; Rasa, Ioan
    In this paper, we define a new generalization of Mellin-Gauss-Weierstrass operators that preserve logarithmic functions. We compute logarithmic moments of the new operators and describe the behavior of the modified operators in some weighted spaces. The weighted approximation properties of operators including weighted approximation and weighted quantitative type approximation properties, using weighted logarithmic modulus of continuity, are presented. Using the Mellin-Gauss-Weierstrass kernel p(., .) as a logarithmic probability density, we study the associated information potential, the expected value E[log p(., .)] and the variance Var[log p(., .)].
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    Quantitative type theorems in the space of locally integrable functions
    (Springer, 2022) Aral, Ali; Ozsarac, Firat; Yilmaz, Basar
    In this work, we introduce a new modulus of continuity for locally integrable function spaces which is influenced by the natural structure of the L-p space. After basic properties of it are given, we obtain a quantitative type theorem for the rate of convergence of convolution type integral operators and iterates of them. Their global smoothness preservation property involving the new modulus of continuity is presented. Finally, the obtained results are applied to Gauss-Weierstrass operators.
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    Reconstruction of Baskakov operators preserving some exponential functions
    (Wiley, 2019) Ozsarac, Firat; Acar, Tuncer
    The present paper deals with a new modification of Baskakov operators in which the functions exp(mu t) and exp(2 mu t), mu > 0 are preserved. Approximation properties of the operators are captured, ie, uniform convergence and rate of convergence of the operators in terms of modulus of continuity, approximation behaviors of the operators exponential weighted spaces, and pointwise convergence of the operators by means of the Voronovskaya theorem. Advantages of the operators for some special functions are presented.
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    Tauberian theorems for iterations of weighted mean summable integrals
    (Springer, 2019) Ozsarac, Firat; Canak, Ibrahim
    Let p be a positive weight function on which is integrable in Lebesgue's sense over every finite interval in symbol: such that for each and For a real- valued function and denote. But the converse of this implication is not true in general. In this paper, we obtain some Tauberian theorems for the weighted mean method of integrals in order that the converse implication holds true. Our results extend and generalize some classical type Tauberian theorems given for Cesaro and logarithmic summability methods of integrals. we say that iteration of weighted mean method determined by the function integrable to a finite number L and we write s(the existence of the limit limx.8 But the converse of this implication is not true in general. In this paper, we obtain some Tauberian theorems for the weighted mean method of integrals in order that the converse implication holds true. Our results extend and generalize some classical type Tauberian theorems given for Cesaro and logarithmic summability methods of integrals.
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    TAUBERIAN THEOREMS FOR THE WEIGHTED MEAN METHOD OF SUMMABILITY OF INTEGRALS
    (Univ Nis, 2020) Ozsarac, Firat; Canak, Ibrahim
    Let q be a positive weight function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0, x) for 0 < x < infinity, in symbol: q is an element of L-loc(1)(R+) such that Q(x) := integral(x)(0) q(t)dt not equal 0 for each x > 0, Q(0) = 0 and Q(x) -> infinity as x -> infinity. Given a real or complex-valued function f is an element of L-loc(1) (R+), we define s(x) := integral(x)(0) f (t)dt and tau((0))(q) (x) := s(x), tau((m))(q) (x) := 1/Q(x) integral(x)(0) tau((m-1))(q) (t)q(l)di (x > 0, m = 1, 2, ...), provided that Q(x) > 0, We say that integral(infinity)(0) (x)dx is summable to L by the m-th iteration of weighted mean method determined by the function q(x), or for short, ((N) over bar, q, m) integrable to a finite number L if x ->infinity(lim) tau((m))(q) (x) = L. In this case, we write s(x) -> L((N) over bar, q, m). It is known that if the limit lim(x ->infinity) (x) = L exists, then lim(x ->infinity) tau((m))(q) (x) = L also exists. However, the converse of this implication is not always true. Some suitable conditions together with the existence of the limit lim(x ->infinity) tau((m))(q) (x), which is so called Tauberian conditions, may imply convergence of lim(x ->infinity) s(x). In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for ((N) over bar, q , m) summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Cesaro summability (C, 1) and weighted mean method of summability ((N) over bar, q) have been extended and generalized.
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    Tauberian theorems for the weighted mean method of summability of integrals
    (Amer Inst Physics, 2019) Canak, Ibrahim; Ozsarac, Firat
    Let q be a positive weight function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0, x) for 0 < x < infinity, in symbol: q is an element of L-loc(1)(R+) such that Q(x) := integral(x)(0)(t)dt # 0 for each x > 0, Q(0) = 0 and Q(x) -> infinity as x -> infinity. Given a real or complex-valued function f is an element of L-loc(1)(R+), we define s(x) := integral(x)(0) f(t)dt and tau((0))(q)(x) := s(x), tau((m))(q)(x) := 1/Q(x) integral(x)(0) tau((m 1))(q)(t)q(t)dt (x > 0, m = 1, 2, ...), provided that Q(x) > 0. We say that integral(infinity)(0) f(x)dx is summable to L by the m-th iteration of weighted mean method determined by the function q(x), or for short, ((N) over bar, q, m) integrable to a finite number L if lim(x ->infinity) tau((m))(q)(x) = L. In this case, we write s(x) -> L((N) over bar, q, m). It is known that if the limit lim(x ->infinity) s(x) = L exists, then lim(x ->infinity) tau((m))(q)(x) = L also exists. However, the converse of this implication is not always true. Some suitable conditions together with the existence of the limit lim(x ->infinity) tau((m))(q)(x), which is so called Tauberian conditions, may imply convergence of lim(x ->infinity) s(x). In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for ((N) over bar, q, m) summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Cesaro summability (C, 1) and weighted mean method of summability ((N) over bar, q) have been extended and generalized.