Some applications of modular convergence in vector lattice setting

TL;DR

This paper explores the application of vector lattice theory and modular convergence to Mellin-type kernels and vector lattice-valued operators, extending previous integral constructions in this mathematical framework.

Contribution

It introduces new applications of modular convergence in vector lattices to Mellin kernels and nonlinear operators, advancing the theoretical understanding of these structures.

Findings

Extended the theory of vector lattices with modular convergence methods.

Applied these methods to Mellin-type kernels and vector lattice-valued operators.

Provided new insights into the integral constructions in this setting.

Abstract

The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an integral given in earlier papers.