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In this note new properties for the Gossez example are presented in regard to its representability, closedness, and maximal monotonicity with respect to the two dual systems it naturally inhabits., Comment: Keywords: monotone operator, dual system, Fitzpatrick function

Extensions of monotone operators into compact sets are provided under a general context of dual systems using nonlinear analysis tools., Comment: version 2

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., Comment: 3 pages

This paper introduces new subdifferential concepts together with their main properties and place with respect to other subdifferential notions.

Abstract Equivalent conditions that make the convex subdifferential maximal monotone are investigated in the general settings of locally convex spaces.

Equivalent conditions that make the normal cone maximal monotone are investigated in the general settings of locally convex spaces. Some consequences such as Bishop Phelps and sum representability results are presented in the last part.

New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space., Comment: 11 pages

In this paper we study, in the relaxed context of locally convex spaces, intrinsic properties of monotone operators needed for the sum conjecture for maximal monotone operators to hold under classical interiority-type domain constraints., Comment: 17pages

The local equicontinuity of an operator $T:X\rightrightarrows X^{*}$ with proper Fitzpatrick function $\varphi_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of $\operatorname*{Pr}\,_{X}(\operatorname*{dom}\varphi_{T})$). The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator defined in a barreled locally convex space.

The local boundedness of classes of operators is analyzed on different subsets directly related to their Fitzpatrick functions and characterizations of the topological vector spaces for which that local boundedness holds is given in terms of the uniform boundedness principle. For example the local boundedness of a maximal monotone operator on the algebraic interior of its domain convex hull is a characteristic of barreled locally convex spaces., Comment: 11pages

A result concerning global extrema in a nonsmooth nonconvex variational problem that appears in applications (e.g. in a large deformation elasticity problem) is investigated in comparison with a result of D.Y. Gao and R.W. Ogden. The tools used are elementary and the results derived improve upon and correct a recent similar result, more precisely, Theorem 4 of the paper "Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem" by the fore-mentioned authors., Comment: This paper has been submitted to ZAMP (Zeitschrift f\"ur angewandte Mathematik und Physik) on April 07, 2010 and was first rejected on December 08, 2010; then, on December 06, 2011 we get the decision "The Editorial Board of ZAMP does not want to pursue this matter any further", without any report. For more details see: http://www.math.uaic.ro/~zalinesc/

In the context of general Banach spaces characterizations for the maximal monotonicity of operators with non-empty domain interior as well as stronger continuity properties for such operators are provided.

In this note we prove that a recent result stated by D.Y. Gao and R.W. Ogden on global minimizers and local extrema in a phase transition problem is false. Our goal is achieved by providing a thorough analysis of the context and result in question and counter-examples., Comment: This paper has been submitted to QJMAM (The Quarterly Journal of Mechanics and Applied Mathematics) on February 19, 2010 and was rejected on October 19, 2010. The reason for the rejection was that "the paper is more like a pure math paper" and this decision was taken mainly after the editor investigated our web-pages. For more details see http://www.math.uaic.ro/~zalinesc/

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3]., Comment: This paper has been submitted to JIMO (Journal of Industrial and Management Optimization) on September 24, 2009 and rejected in May, 2010. The reason for the rejection was that " The authors' view on this issue is known to people in the field". See also http://www.math.uaic.ro/~zalinesc/

On [3, p. 199] one says "We mention parenthetically that the proof of [99, Lemma 41.3] is incorrect, and we do not know whether it, [99, Theorem 41.5] and [99, Theorem 41.6] are true". The previously cited reference [99] is our reference [2]. The aim of this short note is to provide a result that improves upon [2, Lemma 41. 3].

The main focus of this paper is to study multi-valued linear monotone operators in the contexts of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness, negative-infimum, and (dual-) representability are studied and criteria are provided.

Recently in [1] a new class of maximal monotone operators has been introduced. In this note we study domain range properties as well as connections with other classes and calculus rules for these operators we called strongly-representable. While not every maximal monotone operator is strongly-representable, every maximal monotone NI operator is strongly-representable, and every strongly representable operator is locally maximal monotone, maximal monotone locally, and ANA. As a consequence the conjugate of the Fitzpatrick function of a maximal monotone operator is not necessarily a representative function.

This paper is primarily concerned with the problem of maximality for the sum $A+B$ and composition $L^{*}ML$ in non-reflexive Banach space settings under qualifications constraints involving the domains of $A,B,M$. Here $X$, $Y$ are Banach spaces with duals $X^{*}$, $Y^{*}$, $A,B:X\rightrightarrows X^{*}$, $M:Y\rightrightarrows Y^{*}$ are multi-valued maximal monotone operators, and $L:X\to Y$ is linear bounded. Based on the Fitzpatrick function, new characterizations for the maximality of an operator as well as simpler proofs, improvements of previously known results, and several new results on the topic are presented., Comment: 17 pages, submitted to Set-Valued Analysis

The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case., Comment: 3 pages