A Note on Almost Anti-Periodic Functions in Banach Spaces

TL;DR

This paper introduces the concept of almost anti-periodic functions in Banach spaces, providing characterizations and exploring their relationship with anti-periodic and almost periodic functions.

Contribution

It is the first to define and analyze almost anti-periodic functions in Banach spaces, establishing foundational properties and connections with existing classes.

Findings

Characterizations of almost anti-periodic functions

Relationships with anti-periodic and almost periodic functions

Foundational properties established

Abstract

The main aim of this note is to introduce the notion of an almost anti-periodic function in Banach space. We prove some characterizations for this class of functions, investigating also its relationship with the classes of anti-periodic functions and almost periodic functions in Banach spaces.