Hillam's Theorem
If 
(where 
denotes the Closed Interval from 
to 
on the Real Line)satisfies a Lipschitz Condition with constant 
, i.e., if
for all
, then the iteration scheme
where
, converges to a Fixed Point of 
.
References
Falkowski, B.-J. ``On the Convergence of Hillam's Iteration Scheme.'' Math. Mag. 69, 299-303, 1996. Geist, R.; Reynolds, R.; and Suggs, D. ``A Markovian Framework for Digital Halftoning.'' ACM Trans. Graphics 12, 136-159, 1993. Hillam, B. P. ``A Generalization of Krasnoselski's Theorem on the Real Line.'' Math. Mag. 48, 167-168, 1975. Krasnoselski, M. A. ``Two Remarks on the Method of Successive Approximations.'' Uspehi Math. Nauk (N. S.) 10, 123-127, 1955.
- Gauss-Jacobi Mechanical Quadrature
- Gauss-Jordan Elimination
- Gauss-Kummer Series
- Gauss-Kuzmin-Wirsing Constant
- Gauss-Laguerre Quadrature
- Gauss-Manin Connection
- Gauss Map
- Gauss Measure
- Gauss Multiplication Formula
- Gauss Plane
- Gauss-Salamin Formula
- Gauss's Backward Formula
- Gauss's Circle Problem
- Gauss's Class Number Conjecture
- Gauss's Class Number Problem
- Gauss's Constant
- Gauss's Criterion
- Gauss's Double Point Theorem
- Gauss's Equation (Radius Derivatives)
- Gauss's Formula
- Gauss's Formulas
- Gauss's Forward Formula
- Gauss's Harmonic Function Theorem
- Gauss's Hypergeometric Theorem
- Gauss's Inequality