A fixed point theorem for Meir-Keeler contractions in ordered metric spaces

[EN] The purpose of this paper is to present some fixed point theorems for Meir-Keeler contractions in a complete metric space endowed with a partial order. MSC: 47H10.

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

[EN] As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.

Fixed point theorems in partially ordered spaces and aplications

[ES]Recientemente, en la Teoría del punto fijo, han aparecido muchos resultados que obtienen condiciones suficientes para la existencia de un punto fijo si trabajamos con aplicaciones en un conjunto dotado de un orden parcial. Generalmente, estos resultados combinan dos teoremas del punto fijo fundamentales: el Teorema de la contracción de Banach y el Teorema de Knaster-Tarski.

Intrinsic ordering, combinatorial numbers and reliability engineering

[EN]A new algorithm for evaluating the top event probability of large fault trees (FTs) is presented. This algorithm does not require any previous qualitative analysis of the FT. Indeed, its efficiency is independent of the FT logic, and it only depends on the number n of basic system components and on their failure probabilities. Our method provides exact lower and upper bounds on the top event probability by using new properties of the intrinsic order relation between binary strings. The intrinsic order enables one to select binary n-tuples with large occurrence probabilities without necessity to evaluate them. This drastically reduces the complexity of the problem from exponential (2n binary n-tuples) to linear (n Boolean variables)...