Approaching the maximal monotonicity of bifunctions via representative functions

TL;DR

This paper introduces a new approach to maximal monotone bifunctions using representative functions, extending recent results to nonreflexive Banach spaces and providing new insights into the sum of bifunctions.

Contribution

It extends the theory of maximal monotone bifunctions to nonreflexive Banach spaces and presents new results on the sum of bifunctions using representative functions.

Findings

Extended maximal monotonicity results to nonreflexive Banach spaces.

Provided sufficient conditions for maximal monotonicity of bifunctions.

Introduced new results on the sum of two monotone bifunctions.

Abstract

We provide an approach to maximal monotone bifunctions based on the theory of representative functions. Thus we extend to nonreflexive Banach spaces recent results due to A.N. Iusem and, respectively, N. Hadjisavvas and H. Khatibzadeh, where sufficient conditions guaranteeing the maximal monotonicity of bifunctions were introduced. New results involving the sum of two monotone bifunctions are also presented.