A remark on Gwinner's existence theorem on variational inequality problem.
A remark on recent results for finding zeroes of accretive operators.
A study of variational inequalities for set-valued mappings.
A theorem of the Hahn-Banach type and its applications
Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.
A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset of the solution set of the singularly perturbed system. This subset is the set of...
A variant of Newton's method for generalized equations.
Absolutely continuous selections from absolutely continuous set valued map
Abstract Subdifferential Calculus and Semi-Convex Functions
∗ The work is partially supported by NSFR Grant No MM 409/94.We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function.
Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.
An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
An application of a global bifurcation theorem to the existence of solutions for integral inclusions.
An Application of the Stiefel-Whitney Classes to the Proof of a Fixed Point Theorem for Set-Valued Mappings
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.
An existence theorem for differential inclusions on Banach space.
An extension of Fan's fixed point theorem and equilibrium point of an abstract economy
An implicit-function theorem for a class of monotone generalized equations
An improved convergence analysis of a superquadratic method for solving generalized equations.
An intersection theorem for set-valued mappings
Given a nonempty convex set in a locally convex Hausdorff topological vector space, a nonempty set and two set-valued mappings , we prove that under suitable conditions one can find an which is simultaneously a fixed point for and a common point for the family of values of . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.
An Iterative Procedure for Solving Nonsmooth Generalized Equation
2000 Mathematics Subject Classification: 47H04, 65K10.In this article, we study a general iterative procedure of the following form 0 ∈ f(xk)+F(xk+1), where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations in the nonsmooth framework. We prove that this method is locally Q-linearly convergent to x* a solution of the generalized equation 0 ∈ f(x)+F(x) if the set-valued map [f(x*)+g(·)−g(x*)+F(·)]−1 is Aubin continuous...
An order on subsets of cone metric spaces and fixed points of set-valued contractions.
Approximate homomorphisms.