On weak convergence to the fixed point of a generalized asymptotically nonexpansive map.
On weak solutions of functional-differential abstract nonlocal Cauchy problems
The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.
On zeros and fixed points of multifunctions with non-compact convex domains
Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave functions on convex spaces, we obtain extended versions of the existence theorem of H. Ben-El-Mechaiekh [2] on zeros for multifunctions with non-compact domains, the coincidence theorem of S.H. Kum [5] for upper hemicontinuous multifunctions, and the Ky Fan type fixed point theorems due to E. Tarafdar [13].
On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions
Let (X,d) be a metric space. Let Φ be a family of real-valued functions defined on X. Sufficient conditions are given for an α(·)-monotone multifunction to be single-valued and continuous on a weakly angle-small set. As an application it is shown that a γ-paraconvex function defined on an open convex subset of a Banach space having separable dual is Fréchet differentiable on a residual set.
Once more on continuity of maximal monotone mappings
One counterexample concerning the Fréchet differentiability of convex functions on closed sets
One-parameter global bifurcation in a multiparameter problem
Only 3-generalized metric spaces have a compatible symmetric topology
We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.
Open mapping theorem and solution of nonlinear equations in linear normed spaces (Preliminary communication)
Opérateurs asymptotiquement linéaires sur des espaces localement convexes
Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues
Soit un espace localement compact. Tout opérateur dissipatif de domaine dense dans est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur .À tout opérateur vérifiant le principe du maximum positif sur et de domaine assez riche, on associe un opérateur bilinéaire , appelé...
Operational quantities derived from the norm and measures of noncompactness.
Operator type expansion-compression fixed point theorem.
Opial's property and James' quasi-reflexive spaces
Two of James’ three quasi-reflexive spaces, as well as the James Tree, have the uniform -Opial property.
Optimal feedback for perturbed bilinear control problems
Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential...
Optimality Conditions for a Nonlinear Boundary Value Problem Using Nonsmooth Analysis
We study in this paper a Lipschitz control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. The nonlinear part of the equation is governed by a Nemytskij operator defined by a Lipschitzian but possibly nonsmooth function. We prove the existence of optimal controls and obtain a necessary optimality conditions looking somehow to the Pontryagin’s maximum principle. These conditions...
Optimization of Functions on Certain Subsets of Banach Spaces.
Orthogonally additive operators on lattice-normed spaces.