Yazar "Ozsarac, Firat" seçeneğine göre listele

Listeleniyor 1 - 5 / 5
  • Küçük Resim
    Öğe
    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.
  • Küçük Resim
    Öğe
    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.
  • Küçük Resim
    Öğe
    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.
  • Küçük Resim
    Öğe
    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.
  • Küçük Resim
    Öğe
    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.