Approximation theory is a fixpoint theory of general (monotone and non-monotone) operators which generalizes all main semantics of logic programming, default logic and autoepistemic logic. In this paper, we study inductive constructions using operators and show their confluence to the well-founded fixpoint of the operator. This result is one argument for the thesis that Approximation theory is ...

A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a part...

The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds. In this paper, we establish the maximal monotonicity of A+ B provided that A and B are maximally monotone operators such that star(domA)∩ int domB 6= ∅, and A is of type (FPV). We sh...

Results on stability of both local and global metric regularity under set-valued perturbations are presented. As an application, we study (super)linear convergence of a Newtontype iterative process for solving generalized equations. We investigate several iterative schemes such as the inexact Newton’s method, the nonsmooth Newton’s method for semismooth functions, the inexact proximal point alg...

The purpose of this paper is to provide some remarks for the main results of the paper Verma (Appl. Math. Lett. 21:142-147, 2008). Further, by using the generalized proximal operator technique associated with the (A,η,m)-monotone operators, we discuss the approximation solvability of general variational inclusion problem forms in Hilbert spaces and the convergence analysis of iterative sequence...

This paper considers a class of general dynamic programs which satisfies the mono tonicity and contraction assumption, and in which the sets of cost functions and policies are closed under the monotone contraction operators. This class of dynamic programs includes, piecewise linear, affine dynamic programs, partially observable Markov decision processes, and many sequential decision processes u...

In this paper, the notion of closure operators of matroids  is generalized to fuzzy setting  which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...

In any Banach space a monotone operator with a norm-to-weak upper semicontinuous multivalued selection on an open set D is singlevalued and norm-to-norm upper semicontinuous at the points of a dense G subset of D. Monotone operators | and especially a special case of them, subdiierentials of convex functions | play an important role in various parts of nonlinear analysis. One of the often inves...