Riemann–Liouville fractional integral type exponential sampling Kantorovich series

• Published in: Expert systems with applications 2024-03, Vol.238, p.122350, Article 122350
• Main Authors: Kursun, Sadettin, Aral, Ali, Acar, Tuncer
• Format: Article
• Language: English
• Subjects: Exponential sampling series; Fractional integrals; Logarithmic weighted space of functions; Modulus of continuity; Rate of convergence; Voronovskaja-type theorem
• ISSN: 0957-4174
• DOI: 10.1016/j.eswa.2023.122350

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. •Exponential-type sampling series were introduced in the 1980s by optical physicists and engineers to study physically phenomena.