Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators

A New Topological Degree Theory for Densely Defined Quasibounded (s̃+)-perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

Let X be an infinite-dimensional real reflexive Banach space with dual space X∗ and G⊂ X open and bounded. Assume that X and X∗ are locally uniformly convex. Let T : X ⊃ D(T) → 2X be maximal monotone and C : X ⊃ D(C) → X∗ quasibounded and of type (S̃+). Assume that L ⊂ D(C), where L is a dense subspace of X , and 0 ∈ T(0). A new topological degree theory is introduced for the sum T +C. Browder’s...

Semiflows Generated by Lipschitz Perturbations of Non-densely Defined Operators II. Examples

Semiflows Generated by Lipschitz Perturbations of Non-densely Defined Operators I. The Theory

A variety of problems in differential equations ((abstract) functional differential equations, age-dependent population models (with and without delay), evolution equations with boundary conditions e.g.) can be written as semilinear Cauchy problems with a Lipschitz perturbation of a closed linear operator which is not non-densely defined but satisfies the estimates of the Hille&Yosida theorem. ...

Eigenvalues and Ranges for Perturbations of Nonlinear Accretive and Monotone Operators in Banach Spaces

Various eigenvalue and range results are given for perturbations of m-accretive and maximal monotone operators. The eigenvalue results improve and extend some recent results by Guan and Kartsatos, while the range theorem gives an affirmative answer to a recent problem of Kartsatos.

Common Zero Points of Two Finite Families of Maximal Monotone Operators via Proximal Point Algorithms

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...