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Öğe Jackson Type Generalization of Nonlinear Integral Operators(Eudoxus Press, Llc, 2014) Yilmaz, BasarIn this work, we provides a global smoothness preservation result of a Jackson-type generalization of the nonlinear convolution operator defined by Angeloni and Vinti in [4]. Convergence in variation is also studied.Öğe A note on the modified Picard integral operators(WILEY, 2020) Yilmaz, Basar; Aydin Ari, DidemThis study is a natural continuation of modified Picard operators, defined by Agratini et al, preserving an exponential function. Herein, we first show that these operators are approximation processes in the setting of large classes of weighted spaces. Then, we obtain weighted uniform convergence of the operators via exponential weighted modulus of smoothness. Finally, we give, by using the weighted modulus of continuity, the result regarding global smoothness preservation properties for the generalized Picard operators, which based in Agratini et al.Öğe Quantitative type theorems in the space of locally integrable functions(Springer, 2022) Aral, Ali; Özsaraç, Fırat; Yilmaz, BasarIn 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.Öğe RECONSTRUCTION OF TWO APPROXIMATION PROCESSES IN ORDER TO REPRODUCE eax AND e2ax, a > 0(Element, 2021) Yilmaz, Basar; Uysal, Gumrah; Aral, AliWe propose two modifications for Gauss-Weierstrass operators and moment-type operators which fix e(ax) and e(2ax) with a> 0. First, we present moment identities for new operators. Then, we discuss weighted approximation and prove Voronovskaya-type theorems for them in exponentially weighted spaces. Using modulus of continuity in exponentially weighted spaces, we obtain some global smoothness preservation properties. We give a comparison result for Gauss-Weierstrass operators. Finally, we provide some graphical illustrations that show that modified operators perform better than classical ones.Öğe Weighted approximation by modified Picard operators(SPRINGER, 2020) Aral, Ali; Yilmaz, Basar; Deniz, EmreHerein, the aim is to further investigate the properties of the generalized Picard operators introduced in Agratini et al. (Positivity 3(21):1189-1199, 2017). The motivation is based on with the purpose of furnishing appropriate positive approximation processes in the setting of large classes of exponential weighted Lp spaces via different type theorems. For this propose, firstly we give the boundness of the operators, acting from an exponential weighted space into itself. Also, using an exponential weighted modulus of continuity a quantitative type theorem as well as the global smoothness property of the operators are presented. Then, we give pointwise approximation property of the operators at a generalized Lebesgue point. Finally under a certain condition, again the weighted Lp approximation is formulated without using Korovkin type theorem.
