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    Generalized Kantorovich forms of exponential sampling series
    (Springer Basel Ag, 2022) Aral, Ali; Acar, Tuncer; Kursun, Sadettin
    In this paper, we introduce a new family of operators by generalizing Kantorovich type of exponential sampling series by replacing integral means over exponentially spaced intervals with its more general analogue, Mellin Gauss Weierstrass singular integrals. Pointwise convergence of the family of operators is presented and a quantitative form of the convergence using a logarithmic modulus of continuity is given. Moreover, considering locally regular functions, an asymptotic formula in the sense of Voronovskaja is obtained. By introducing a new modulus of continuity for functions belonging to logarithmic weighted space of functions, a rate of convergence is obtained. Some examples of kernels satisfying the obtained results are presented.
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    Öğe
    Riemann-Liouville fractional integral type exponential sampling Kantorovich series
    (Pergamon-Elsevier Science Ltd, 2024) Kursun, Sadettin; Aral, Ali; Acar, Tuncer
    In the present paper, we introduce a new family of sampling Kantorovich type operators using fractional-type integrals. We study approximation properties of newly constructed operators and give a rate of convergence via a suitable modulus of continuity. Furthermore, we obtain an asymptotic formula considering locally regular functions. Secondly, we deal with logarithmic weighted spaces. By using a certain weighted logarithmic modulus of continuity, we obtain a rate of convergence and give a quantitative form of Voronovskaja-type theorem considering the remainder of Mellin-Taylor's formula. Moreover, we give a relation between generalized exponential sampling operators and newly constructed operators. Finally, we present some examples of kernels satisfying the obtained results. The results are examined by illustrative numerical table and graphical representations.
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    Öğe
    Riemann–Liouville fractional integral type exponential sampling Kantorovich series
    (Elsevier Ltd, 2024) Kursun, Sadettin; Aral, Ali; Acar, Tuncer
    In the present paper, we introduce a new family of sampling Kantorovich type operators using fractional-type integrals. We study approximation properties of newly constructed operators and give a rate of convergence via a suitable modulus of continuity. Furthermore, we obtain an asymptotic formula considering locally regular functions. Secondly, we deal with logarithmic weighted spaces. By using a certain weighted logarithmic modulus of continuity, we obtain a rate of convergence and give a quantitative form of Voronovskaja-type theorem considering the remainder of Mellin–Taylor's formula. Moreover, we give a relation between generalized exponential sampling operators and newly constructed operators. Finally, we present some examples of kernels satisfying the obtained results. The results are examined by illustrative numerical table and graphical representations. © 2023 Elsevier Ltd