Keys to success in an example of inter-competitor cooperation: The case of the "Big Seven" basque chefs

The case of the top chefs relates the two areas that are apparently most distant, nutrition and health technology. It is the element that binds[3] the four, making them into a single whole. The results achieved by our chefs, in terms of their individual and collective success and their international projection of the image of the Basque Country comprise a goal to which other industries in the region should aspire. It is therefore our plan to apply the keys to this successful inter-competitor cooperation to development of the health technology industry. At the same time, we want to fulfil one of the aims that have been established for the food area: to make use of the country’s gastronomy-related assets.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical