In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.
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In this paper we define the operation G on the set of all generalized hypersubstitutions and investigate some algebraic-structural properties of the set of all generalized hypersubstitutions and of some submonoids M of the set of all generalized hypersubstitutions, respectively.
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In the paper the duality of the the notions of (higher) hypergraph and (higher) partition is shown. Both higher level hypergraphs and higher partitions are characterized algebr aically as left and right regular bands.
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