Weak conditions for the convergence of iterations to solutions of equations on partially ordered topological spaces.
Weak convergence theorems of three iterative methods for strictly pseudocontractive mappings of Browder-Petryshyn type.
Weaker convergence conditions for the secant method
We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.
Weakly coercive mappings sharing a value
Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined between any two Banach spaces over has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout the entire space. The proof of the result is constructive and is based upon a continuation method.