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The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

Miroslaw Lustyk, Julian Janus, Marzenna Pytel-Kudela, Anatoliy Prykarpatsky (2009)

Open Mathematics

The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated...

The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.

Luis Alvarez, Jesús Ildefonso Díaz (2003)

RACSAM

In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.

Über schwach zyklische Abbildungen in nichtlinearen Produkträumen und einige Monotonieaussagen

Christian P. Ullrich (1979)

Aplikace matematiky

In der Arbeit werden einige Eigenschaften der sog. schwach zyklischen Vektorfunktionen untersucht. Die allgemeine Deffinition einer schwach zyklischen Funktion enthält als einen Spezialfall Funktionen der Form A x mit einer schwach zyklischen Matrix A . Es werden insbesondere Monotonie Eigenschaften schwach zyklischer Funktionen betrachtet, wobei die Monotonie in verallgemeinertem Sinn definiert wird.

Weaker convergence conditions for the secant method

Ioannis K. Argyros, Saïd Hilout (2014)

Applications of Mathematics

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

J. M. Soriano (2011)

Czechoslovak Mathematical Journal

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 𝕂 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.

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