Yazar "Rasa, Ioan" seçeneğine göre listele

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    Approximation by k-th order modifications of Szász-Mirakyan operators
    (Akademiai Kiado Rt, 2016) Acar, Tuncer; Aral, Ali; Rasa, Ioan
    In this paper, we study the k-th order Kantorovich type modication of Szasz-Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szasz-Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.
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    Approximation properties of Szasz-Mirakyan operators preserving exponential functions
    (Springer, 2019) Aral, Ali; Inoan, Daniela; Rasa, Ioan
    This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, 10.1007/s00009-016-0804-7) where Szasz-Mirakyan operators preserving exponential functions are defined. As a first result, we show that the sequence of the norms of the operators, acting on weighted spaces having different weights, is uniformly bounded. Then, we prove Korovkin type approximation theorems through exponential weighted convergence. The uniform weighted approximation errors of the operators and their derivatives are characterized for exponential weights. Furthermore we give a Voronovskaya type theorem for the derivative of the operators.
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    Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation
    (North Univ Baia Mare, 2022) Acu, Ana Maria; Aral, Ali; Rasa, Ioan
    This paper includes Voronovskaya type results and convergence in variation for the exponential Bernstein Kantorovich operators. The Voronovskaya type result is accompanied by a relation between the mentioned operators and suitable auxiliary discrete operators. Convergence of the operators with respect to the variation seminorm is obtained in the space of functions with bounded variation. We propose a general framework covering the results provided by previous literature.
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    Iterated Boolean Sums of Bernstein Type Operators
    (TAYLOR & FRANCIS INC, 2020) Acar, Tuncer; Aral, Ali; Rasa, Ioan
    The approximation of functions using linear positive operators is affected by saturation. The quality of approximation offered by iterated Boolean sums increases with the regularity of the function. We present some qualitative and quantitative results concerning the approximation by such Boolean sums. The general results are illustrated by examples.
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    The new forms of Voronovskaya's theorem in weighted spaces
    (Springer, 2016) Acar, Tuncer; Aral, Ali; Rasa, Ioan
    The Voronovskaya theorem which is one of the most important pointwise convergence results in the theory of approximation by linear positive operators (l.p.o) is considered in quantitative form. Most of the results presented in this paper mainly depend on the Taylor's formula for the functions belonging to weighted spaces. We first obtain an estimate for the remainder of Taylor's formula and by this estimate we give the Voronovskaya theorem in quantitative form for a class of sequences of l.p.o. The Gruss type approximation theorem and the Gruss-Voronovskaya-type theorem in quantitative form are obtained as well. We also give the Voronovskaya type results for the difference of l.p.o acting on weighted spaces. All results are also given for well-known operators, Szasz-Mirakyan and Baskakov operators as illustrative examples. Our results being Voronovskaya-type either describe the rate of pointwise convergence or present the error of approximation simultaneously.
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    New properties of operators preserving exponentials
    (Springer-Verlag Italia Srl, 2023) Acu, Ana-Maria; Aral, Ali; Rasa, Ioan
    The paper is devoted to a sequence of positive linear operators preserving two exponential functions. We investigate their iterates, invariant measures, Kantorovich modifications, eigenstructure, and global smoothness preservation properties.
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    On approximation by some Bernstein-Kantorovich exponential-type polynomials
    (Springer, 2019) Aral, Ali; Otrocol, Diana; Rasa, Ioan
    Since the introduction of Bernstein operators, many authors defined and/or studied Bernstein type operators and their generalizations, among them are Morigi and Neamtu (Adv Comput Math 12:133-149, 2000). They proposed an analog of classical Bernstein operator and proved some convergence results for continuous functions. Herein, we introduce their integral extensions in Kantorovich sense by replacing the usual differential and integral operators with their more general analogues. By means of these operators, we are able to reconstruct the functions which are not necessarily continuous. It is shown that the operators form an approximation process in both C [0, 1] and L-p,L-mu [0, 1], which is an exponentially weighted space. Also, quantitative results are stated in terms of appropriate moduli of smoothness and K-functionals. Furthermore, a quantitative Voronovskaya type result is presented.
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    On differences of linear positive operators
    (Springer Basel Ag, 2019) Aral, Ali; Inoan, Daniela; Rasa, Ioan
    In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these operators in quantitative form. Our estimates involve an appropriate K-functional and a weighted modulus of smoothness. Similar estimates are obtained for Chebyshev functional of these operators as well. All considerations are based on rearrangement of the remainder in Taylor's formula. The obtained results are applied for some well known linear positive operators.
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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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    Power series of Beta operators
    (Elsevier Science Inc, 2014) Acar, Tuncer; Aral, Ali; Rasa, Ioan
    In this paper we investigate the power series of Beta operators. We first study the convergence of this series and describe the Voronovskaya operator A and the inverse Voronovskaya operator. Then, a quantitative convergence result for the inverse Voronovskaya operator via smoothing approach is given. The power series is also related to the resolvent of A and the semigroup generated by A. (C) 2014 Elsevier Inc. All rights reserved.
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    Power Series of Positive Linear Operators
    (Springer Basel Ag, 2019) Acar, Tuncer; Aral, Ali; Rasa, Ioan
    We describe a unifying approach for studying the power series of the positive linear operators from a certain class. For the same operators, we give simpler proofs of some known ergodic theorems.