Abstract. Some prediction properties of the t-transformation of Levin are analyzed for two kinds of limiting processes. It is shown under certain circumstances that when the t-transformation is applied to a power series, the coefficients of the Maclaurin series of the rational approximation obtained approximate those of the given series with increasing accuracy. Theoretical and numerical exampl...

In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) normalized holomorphic bi-univalent functions in open unit disk U, which are associated with Bazilevič λ-pseudo-starlike as well Horadam polynomials. We estimate second third coefficients Taylor-Maclaurin expansions belonging to function class, here. Furthermore, esta...

Let R+ = (0,∞) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 ∈ M, we say that a function f : R+ → R+ is (m1, m2)-convex if f(m1(x, y)) ≤ m2(f(x), f(y)) for all x, y ∈ R+. The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1, m2)-convexit...