The development of the unified version mixing maps between arbitrary sets
Keywords:Composition theorem, Hausdorff topological space, Nonlinear mixing maps, Pietsch Domination theorem, Set theory
The concepts of nonlinear mixed summable families and maps for the spaces that only non-void sets are developed. Several characterizations of the corresponding concepts are achieved and the proof for a general Pietsch Domination-type theorem is established. Furthermore, this work has presented plenty of composition and inclusion results between different classes of mappings in the abstract settings. Finally, a generalized notation of mixing maps and their characteristics are extended to a more general setting.