This note is an addendum to Sum theorems for monotone operators and convex functions. In it, we prove some new results on convex functions and monotone operators, and use them to show that several of the constraint qualifications considered in the preceding paper are, in fact, equivalent. Introduction We continue with the notation and the numbering of [4]. For the moment, we shall assume that E...

In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar’s constraint qualification holds. In this paper, we prove the maximal monotonicity of A+B provided that A and B are maximal monotone operators such that domA ∩ int domB ̸= ∅, A+NdomB is of type (FPV), and domA∩domB ⊆ domB. The proof ...

We propose an inexact version of the proximal point method and study its properties in nonreflexive Banach spaces which are duals of separable Banach spaces, both for the problem of minimizing convex functions and of finding zeroes of maximal monotone operators. By using surjectivity results for enlargements of maximal monotone operators, we prove existence of the iterates in both cases. Then w...

In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

This paper introduces new similarity classifiers using the Heronian mean, and the generalized Heronian mean operators. We examine the use of these operators at the aggregation step within the similarity classifier. The similarity classifier was earlier studied with other operators, in particular with an arithmetic mean, generalized mean, OWA operators, and many more. The two classifiers here ar...

The classical Loewner’s theorem states that operator monotone functions on real intervals are described by holomorphic the upper half-plane. We characterize local order isomorphisms domains biholomorphic automorphisms of generalized half-plane, which is collection all operators with positive invertible imaginary part. describe such maps in an explicit manner, and examine properties maximal isom...