Generic nondegeneracy in convex optimization [PDF]
Proc. Amer. Math. Soc. 139 (2011), 2519-2527, 2010 We show that minimizers of convex functions subject to almost all linear perturbations are nondegenerate. An analogous result holds more generally, for lower-C^2 functions.
arxiv
Maximal monotone operators with non-empty domain interior; characterizations and continuity properties [PDF]
arXiv, 2011 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.
arxiv
Note on the existence theory for evolution equations with pseudo-monotone operators [PDF]
arXiv, 2015 In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.
arxiv
Maximal monotonicity of the subdifferential of a convex function: a direct proof [PDF]
Journal of Convex Analysis 24 (2017), No. 4, 1307--1311, 2016 We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
arxiv
New fixed point results on $G$-metric spaces [PDF]
arXiv, 2017 In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point.
arxiv
A priori estimates for the Fitzpatrick function [PDF]
arXiv, 2017 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.
arxiv
Maximal monotone normal cones in locally convex spaces [PDF]
arXiv, 2019 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.
arxiv
Examples for uniformly monotone operators arising in nonlinear elliptic and parabolic problems [PDF]
arXiv, 2009 We show some examples for uniformly monotone operators arising in weak formulation of nonlinear elliptic and parabolic problems. Besides the classical $p$-Laplacian some other less known examples are given which might be of interest because of applications.
arxiv
A new characterization of partial metric completeness [PDF]
arXiv, 2019 In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.
arxiv
Recent developments in the fixed point theory of enriched contractive mappings. A survey [PDF]
arXivThe aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings established by the authors and their collaborators by using this technique; and third, to survey some related ...
arxiv