Elements of Real Analysis

By R. Bartle, D. R. Sherbert. 2006

683 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9514570c4c0477a1ef8e5f463fb924f9e0327c6e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

Citations in the corpus

A survey on the Weierstrass approximation theorem (2006, background): “The proofs more commonly taken at level of undergraduate courses in Mathematics are those of Fejér (1900) and Bernstein (1912) (see, for example [4], [7], [16] or [20]).”
Distributed Interference-Aware Energy-Efficient Power Optimization (2011, background): “We know that when a contraction mapping has a fixed point, the fixed point is unique [16].”
Kinship, Incentives, and Evolution (2010, background): “Bartle, 1976 ), guarantees local uniqueness of the solution to (3).”
Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer (2013, neutral): “Invoking the implicit function theorem [79], for the reference trajectory yd satisfying Assumption 1, there exists a unique local solution u = β(x, ξ) ∈ Ωu ⊂ R such that f(x, β(x, ξ)) + ξ = 0 for all x0 ∈ Ωx0 ⊂ R.”
From caging to grasping (2011, background): “From a practical perspective, however, this does not impose any hard constraint, since algebraic functions are dense in the space of continuous functions (Bartle 1964), which means that we can always approximate as close as we want any continuous non-algebraic function by an algebraic one.”
Neural network approximation of piecewise continuous functions: application to friction compensation (1997, background): “denote the p-norm by p . The supremum norm of f(x), over S, is defined as [ 4 ]”
Large deviations of a modified Jackson network: Stability and rough asymptotics (2005, background): “GEORGIA INSTITUTE OFTECHNOLOGY 765 FERSTDRIVE ATLANTA , GEORGIA 30332-0205 USA DEPARTMENT OFMATHEMATICS AND STATISTICS UNIVERSITY OF OTTAWA P.O. BOX 450 OTTAWA , ONTARIO K1N6N5 CANADA E-MAIL : dmdsg@uottawa.ca”