The unified version of mixing maps between non-void sets

TL;DR

This paper develops nonlinear concepts of mixed summable families and maps for non-void sets, providing characterizations, a Pietsch Domination-type theorem, and extending mixing maps to a broader setting.

Contribution

It introduces a unified framework for mixing maps between non-void sets, including characterizations, domination theorems, and generalized notions of mixing maps.

Findings

Established a Pietsch Domination-type theorem for the new concepts.

Provided composition and inclusion results for classes of mappings.

Extended the notion of mixing maps to a more general setting.

Abstract

The nonlinear concepts of 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.