The generalized topological degree theory is based on the Brouwer and Leray-Schauder degrees. It can be deened for general classes of mappings. The purpose of this article is twofold. One goal is to deene the topological degree for maximal monotone operators. Particular attention is paid to the continuation methods for this kind of operators and real functions of convex type. This allows us to ...

We present results for the existence of solutions for variational inequalities given by generalized monotone operators. As a consequence we establish surjectivity, and we obtain, in particular, results for the existence of zeroes of some class of set-valued operators. Furthermore, by strengthening the continuity assumption on the operator, we deduce its surjectivity without any monotonicity ass...

In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.

Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood and analyzed from the alternative viewpoint of firmly nonexpansive mappings, which were found to be precisely the resolvents of monotone operators. For examp...

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...

We propose a generalized proximal point algorithm (PPA), in the generic setting of finding a root of a maximal monotone operator. In addition to the classical PPA, a number of benchmark operator splitting methods in the PDE and optimization literatures can be retrieved by this generalized PPA scheme. We establish the convergence rate of this generalized PPA scheme under different conditions, in...

This paper presents and analyzes a strongly convergent approximate proximal point algorithm for finding zeros of maximal monotone operators in Hilbert spaces. The proposed method combines the proximal subproblem with a more general correction step which takes advantage of more information on the existing iterations. As applications, convex programming problems and generalized variational inequa...

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis fixed point algorithms. Various properties conically are systematically investigated, particular, stability under relaxations, convex combinations compositions. derive averagedness resolvents generalized monotone operators. These then utilized order to analyze proximal algorithm, forwar...