From Third Note:
It is Time to Think of S-convexity
Convexity has captured the hearts of pure and applied mathematicians because it is a very geometric concept. Professor Stanley F. Gudder, already in 1977, discussed using convexity in studies that connect to social, behavioural, and physical sciences. Professor Robert E. Jamison-Waldner talked about mathematical methods that are based on the convexity phenomenon in 1983. S-convexity was not a proper extension of convexity until 2001, when we started working with the concept. We have found many fallacies and inaccuracies that we have been addressing since then. The paper Minima Domain Intervals ended up fixing things in the realm of convexity as well, basic items, such as the analytical definition, and the paper First Note ended up fixing the geometric definition for convexity, so that S-convexity became a really useful and beautiful concept for Pure and Applied Mathematics. In this talk, we would like to discuss our final results on the analysis of the shape and the re-wording of the definitions.