Fixed points of dynamic processes of set-valued F-contractions and application to functional equations

The article is a continuation of the investigations concerning F-contractions which have been recently introduced in [Wardowski in Fixed Point Theory Appl. 2012:94,2012]. The authors extend the concept of F-contractive mappings to the case of nonlinear F-contractions and prove a fixed point theorem via the dynamic processes. The paper includes a non-trivial example which shows the motivation for such investigations. The work is summarized by the application of the introduced nonlinear F-contractions to functional equations

On the existence of fixed points that belong to the zero set of a certain function

Let T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem

Fixed point theorems for \u3b1-set-valued quasi-contractions in b-metric spaces

Recently, Samet et al. [B. Samet, C. Vetro and P. Vetro, Fixed point theorems for alpha-psi-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165] introduced the notion of alpha-psi-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notions of alpha-set-valued contraction and alpha-set-valued quasi-contraction and we give some fixed point theorems for such classes of mappings in the setting of b-metric spaces and ordered b-metric spaces. The presented theorems extend, unify and generalize several well-known comparable results in the existing literature

Multi-valued F-contractions in 0-complete partial metric spaces with application to Volterra type integral equation

We study the existence of fixed points for multi-valued mappings that satisfy certain generalized contractive conditions in the setting of 0-complete partial metric spaces. We apply our results to the solution of a Volterra type integral equation in ordered 0-complete partial metric spaces

Analysis of the severe flood of 13t-16th October 2000 in Piedmont (Italy)

During the 13th-16th of October 2000 a disastrous flood occurred in the whole Piedmont associated with heavy rainfall over the North-Western Alpine chain in successive episodes spanning the whole period. The event was originated by a Southern, strong and moist, upper flow established over North-Western Italy, associated at lower layers with an eastern rotation of the air flow and consequently strong convergence on the western Po Valley. The high temperature of the Mediterranean Sea caused a high rate of moisture enrichment of the air mass moving towards Piedmont. The most intense rainfall (values larger than 600 mm in 96 hours have been re ported) occurred over the mountainous regions, where the high temperatures forced the snow-rain threshold at very high altitudes. This event was one of the most intense events of the last 200 years in the Piedmont area. The majority of the basins suffered strong flood episodes; most of the mountainous portion of the basins and also part of the city of Turin down the Po Valley were seriously damaged by the strong rainfalls.</jats:p