A generalized solution of a nonconvex minimization problem and its stability
A geometric lower bound on Grad’s number
In this note we provide a new geometric lower bound on the so-called Grad’s number of a domain in terms of how far is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.
A geometric lower bound on Grad's number
In this note we provide a new geometric lower bound on the so-called Grad's number of a domain Ω in terms of how far Ω is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.
A hybrid inertial projection-proximal method for variational inequalities.
A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces.
A hybrid iterative scheme for variational inequality problems for finite families of relatively weak quasi-nonexpansive mappings.
A hybrid method for monotone variational inequalities involving pseudocontractions.
A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequality problem.
A hybrid projection-proximal point algorithm.
A hybrid proximal point three-step algorithm for nonlinear set-valued quasi-variational inclusions system involving -accretive mappings.
A Lagrange multiplier theorem and a sandwich theorem for convex relations.
A Landesman-Lazer alternative theorem for a class of optimization problems.
A Leontief-type input-output inclusion.
A level set method in shape and topology optimization for variational inequalities
The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology...
A Lipschitz function which is on a.e. line need not be generically differentiable
We construct a Lipschitz function f on X = ℝ ² such that, for each 0 ≠ v ∈ X, the function f is smooth on a.e. line parallel to v and f is Gâteaux non-differentiable at all points of X except a first category set. Consequently, the same holds if X (with dimX > 1) is an arbitrary Banach space and “a.e.” has any usual “measure sense”. This example gives an answer to a natural question concerning the author’s recent study of linearly essentially smooth functions (which generalize essentially smooth...
A mathematical model for the recovery of human and economic activities in disaster regions
In this paper a model for the recovery of human and economic activities in a region, which underwent a serious disaster, is proposed. The model treats the case that the disaster region has an industrial collaboration with a non-disaster region in the production system and, especially, depends upon each other in technological development. The economic growth model is based on the classical theory of R. M. Solow (1956), and the full model is described as a nonlinear system of ordinary differential...
A Mean Value Theorem for non Differentiable Mappings in Banach Spaces
We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition....
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part II.
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part I.
A minimax formula for the principal eigenvalues of Dirichlet problems and its applications.