• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.45-56
• /
• 2021

D.S. Kim et al. [9] considered some identities and relations for Korobov type numbers and polynomials. In this work, we investigate the degenerate Korobov type Changhee polynomials and the (p,q)-poly-Korobov polynomials. We give a generalization of the Korobov type Changhee polynomials and the (p,q) poly-Korobov polynomials. We prove some properties and identities and explicit relations for these polynomials.

• Kyungpook Mathematical Journal
• /
• v.64 no.1
• /
• pp.57-68
• /
• 2024

Let V₃(z, f) and 𝜎⁽¹⁾₃(z, f) be the cubic polynomials representing, respectively, the 3rd de la Vallée Poussin mean and the 3rd Cesàro mean of order 1 of a power series f(z). If 𝒦 denotes the usual class of convex univalent functions in the open unit disk centered at the origin, we show that, in general, V₃(z, f) ⊀ 𝜎⁽¹⁾₃(z,f), for all f ∈ 𝒦. Making use of polylogarithms, we identify a transformation, Λ : 𝒦 → 𝒦, such that V₃(z, Λ(f)) ≺ 𝜎⁽¹⁾₃(z, Λ(f)) for all f ∈ 𝒦. Here '≺' stands for subordination between two analytic functions.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.489-508
• /
• 2020

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.315-326
• /
• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.