Annoucements • Office = MATH 221 (Directly above the Mathematics Department Office.) • Email = [email protected] • Text = “Baby Rudin” – Principles of Mathematical Analysis 3/e by Walter Rudin • Course Website = “http://www.math.ubc.ca/∼feldman/m321/” • Topics: – Riemann-Stieltjes integral (§6) – Sequences & Series of functions (§7) – Power Series, Special Functions, Fourier Series (§8) – Ano...

(h(tj−1) can be replaced by h(sj), for any sj ∈ [tj−1, tj ].) As n gets larger and larger while the partition gets finer and finer, the approximating sum to the true area under the function becomes exact. This “dt” integration can be generalized to increments “dG(t)” of (say) any monotone increasing function G(t) by using G(tj) − G(tj−1) in place of tj − tj−1 yielding the so-called Riemann-Stie...

The Stieltjes constants γk appear in the coefficients in the regular part of the Laurent expansion of the Riemann zeta function ζ(s) about its only pole at s = 1. We present an asymptotic expression for γk for k 1. This form encapsulates both the leading rate of growth and the oscillations with k. Furthermore, our result is effective for computation, consistently in close agreement (for both ma...

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized f...

In this article, we study a class of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different parameters. Based on the Guo-Krasnosel’skii fixed point theorem, some new results on the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different parameters on ...

*Correspondence: [email protected] 1College of Science, China Agricultural University, Beijing, 100083, China Full list of author information is available at the end of the article Abstract This paper investigates the existence of concave positive solutions and establishes corresponding iterative schemes for a third-order boundary value problem with Riemann-Stieltjes integral boundary conditions....

In this paper we provide sharp bounds for the error in approximating the Riemann-Stieltjes integral R b a f (t) du (t) by the trapezoidal rule f (a) + f (b) 2 [u (b) u (a)] under various assumptions for the integrand f and the integrator u for which the above integral exists. Applications for continuous functions of selfadjoint operators in Hilbert spaces are provided as well. 1. Introduction I...