In the study of nonexpansive mappings and fixed point theory the domain of the mapping is usually assumed to be bounded or, as in certain approximation results (see, e.g., [20]), fixed points are assumed to exist. However in [21] Penot used uniform asymptotic concepts which he had earlier introduced in [22] to extend the Browder-Göhde-Kirk theorem to unbounded sets. The term “asymptotic” is use...

Measures of risk appear in two categories: Risk capital measures serve to determine the necessary amount of risk capital in order to avoid ruin if the outcomes of an economic activity are uncertain and their negative values may be interpreted as acceptability measures (safety measures). Pure risk measures (risk deviation measures) are natural generalizations of the standard deviation. While pur...

While it is often claimed that any connection between visual art and music is strictly subjective, this paper attempts to prove that motion can be used to connect the two domains in a manner that, though not objective in the true sense of the word, will nevertheless be perceived in a similar fashion by multiple people. The paper begins with a brief history of attempts to link audio and visuals,...

This paper proposes three enlargements of the conventional Moreau–Rockafellar subdifferential: sup-, sup⋆- and symmetric subdifferentials. They satisfy most fundamental properties convexity, weak∗-closedness and, if function is bounded, weak∗-compactness. Moreover, they are nonempty for Rainwater function, possess certain calculus rules, provide necessary sufficient optimality conditions not ne...

In this short note, we derive an upper estimate of Clarke's subdifferential marginal functions in Banach spaces. The structure the is very similar to other results already obtained literature. novelty lies on fact that our assertions general spaces, and avoid use Asplund assumption.

For example among the gastropods 80% of the species found in the lake are endemic. Most diversity is displayed in the family Thiaridae. The genus Lavigeria it is the most common thiarid genus and at the same time the most diverse (Michel 1995). It has an estimated species diversity of 20 or more endemic species (Michel & Todd, in prep). The often sympatric species show many shell morphological ...