The development of the unified version mixing maps between arbitrary sets

Salam Adel Al-Bayati; Akram Al-Sabbagh; Omar Al-Tameemi; Manaf Adnan Saleh

doi:10.24996/ijs.2022.63.3.33

Authors

Salam Adel Al-Bayati Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, 10072, Iraq https://orcid.org/0000-0003-1236-1201
Akram Al-Sabbagh Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, 10072, Iraq https://orcid.org/0000-0002-7731-4791
Omar Al-Tameemi Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, 10072, Iraq https://orcid.org/0000-0001-5611-6916
Manaf Adnan Saleh Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, 10072, Iraq https://orcid.org/0000-0003-3046-3439

DOI:

https://doi.org/10.24996/ijs.2022.63.3.33

Keywords:

Composition theorem, Hausdorff topological space, Nonlinear mixing maps, Pietsch Domination theorem, Set theory

Abstract

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.