Viacheslav Kalashnikov, A. Talman, N. Kalashnykova, L. Alanís-López
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引用次数: 0
Abstract
The paper develops the extensions of both the antipodal (Borsuk–Ulam) theorem and Browder theorem to the cases embracing star-shaped domains of the studied mappings and a multi-valued nature of the latter.To be more specific, by making use of the triangulation procedure, we spread out the antipodal and fixed-point theorems to the case of not necessarily convex (star-shaped) domains. In addition, similar extensions are obtained for multi-valued mappings defined over star-shaped sets. Moreover, a directt algorithm shaping the required connected path of the zero points of the mapping has been designed, and its convergence demonstrated.
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