Maximality of the sum of the monotone operator of type (FPV) and a maximal monotone operator

TL;DR

This paper proves that the sum of a maximal monotone operator of type (FPV) and another maximal monotone operator is maximal monotone under certain conditions, extending previous results without requiring convexity of A's domain.

Contribution

It establishes the maximal monotonicity of the sum of two operators with one of type (FPV) under Rockafellar's constraint qualification, removing the convexity assumption.

Findings

Sum of two maximal monotone operators is maximal monotone under (FPV) conditions.

The sum operator retains type (FPV) without convexity assumptions.

Provides a resolution to a question posed by Borwein and Yao.

Abstract

Here, question raised by Borwein and Yao has been settled by establishing that the sum of two maximal monotone operators A and B is maximal monotone with the condition that A is of type (FPV) and satisfies Rockafellar's constraints qualification. Also we have proved that A+B is of type (FPV) without assuming convexity on the domain of A.