The sum theorem for maximal monotone operators in reflexive Banach spaces revisited

TL;DR

This paper provides a new, shorter proof demonstrating that the Minkowski sum of two maximal monotone operators remains maximal monotone in reflexive Banach spaces, under the classical interiority condition.

Contribution

It introduces a more concise proof for the maximal monotonicity of the sum of two maximal monotone operators in reflexive Banach spaces, improving upon existing proofs.

Findings

Shorter proof of maximal monotonicity of operator sums

Validation under classical interiority condition

Enhanced understanding of operator sum properties

Abstract

Our goal is to present a new shorter proof for the maximal monotonicity of the Minkowski sum of two maximal monotone multi-valued operators defined in a reflexive Banach space under the classical interiority condition involving their domains.