Scopus
🔓 Açık Erişim
On Korovkin-Type Theorems Including Exponential Test Functions on Infinite Intervals Through Power Series Convergence
Mediterranean Journal of Mathematics · Şubat 2026
Makale Bilgileri
DergiMediterranean Journal of Mathematics
Yayın TarihiŞubat 2026
Cilt / Sayfa23
Scopus ID2-s2.0-105027367358
Erişim🔓 Açık Erişim
Özet
Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which provide simple and elegant criteria for convergence by testing only on a small set of functions. Motivated by these classical results and their extensions, we focus on versions that preserve exponential functions and incorporate modern summability techniques. In this paper, we establish Korovkin-type theorems involving exponential test functions by employing power series convergence and a special case thereof. By considering approximation through Borel-type power series convergence via integral summability, we provide an alternative framework that applies in cases where classical convergence or ordinary Borel convergence fails, and we offer a comparative analysis of the corresponding theorems. We also present illustrative examples in which the classical results fail, while the proposed approach remains applicable. In addition, the rate of convergence is analyzed through the modulus of continuity.
Yazarlar (2)
1
Di̇lek Söylemez
2
Mehmet Ünver
ORCID: 0000-0002-0857-1006
Anahtar Kelimeler
Integral summability
Korovkin type theorem
Power series convergence
Rate of the convergence
Kurumlar
Ankara Üniversitesi
Ankara Turkey
Selçuk Üniversitesi
Selçuklu Turkey