Unbounded linear monotone operators on nonreflexive Banach spaces.
Une fonction β-lipschitzienne qui n'est pas une perturbation compacted'une fonction dissipative
Résumé. On présente une fonction continue f: c₀ → c₀ qui satisfait à une condition lipschitzienne par rapport à la mesure de non-compacité de Hausdorff (ou Kuratowski), mais telle que f n'est pas la somme d'une fonction dissipative et d'une fonction compacte. Cet exemple attache de l'importance au théorème d'existence de Sabina Schmidt (1989) pour des équations différentielles dans les espaces de Banach.
Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes
In this Note we first establish a result on the structure of the set of fixed points of a multi-valued contraction with convex values. As a consequence of this result, we then obtain the following theorem: Let , be two real Banach spaces and let be a continuous linear operator from onto . Put: . Then, for every and every lipschitzian operator , with Lipschitz constant such that , the set is non-empty and arc wise connected.
Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly Lipschitzian semigroups. I.
Uniform asymptotic normal structure, the uniform semi-opial property, and fixed points of asymptotically regular uniformly Lipschitzian semigroups. II.
Uniform Convergence of the Newton Method for Aubin Continuous Maps
* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that the derivative of f is Lipschitz...
Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu
We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.
Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces
We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.
Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder function spaces
We show that the generator of any uniformly bounded set-valued Nemytskij composition operator acting between generalized Hölder function metric spaces, with nonempty, bounded, closed, and convex values, is an affine function.
Uniformly Continuous Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz
We show that any uniformly continuous and convex compact valued Nemytskiĭ composition operator acting in the spaces of functions of bounded φ-variation in the sense of Riesz is generated by an affine function.
Uniformly convex and uniformly smooth convex functions
Uniformly normal structure and fixed points of uniformly Lipschitzian mappings
Unique solution of periodic boundary value problems.
Unitary dilation and fixed point theorem
Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions
In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.
Upper Semicontinuous Perturbations of m-accretive Operators and Differential Inclusions with Dissipative Right-hand Side
Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces.
Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces.
Variational inequalities in noncompact nonconvex regions
In this paper, a general existence theorem on the generalized variational inequality problem GVI(T,C,ϕ) is derived by using our new versions of Nikaidô's coincidence theorem, for the case where the region C is noncompact and nonconvex, but merely is a nearly convex set. Equipped with a kind of V₀-Karamardian condition, this general existence theorem contains some existing ones as special cases. Based on a Saigal condition, we also modify the main theorem to obtain another existence theorem on GVI(T,C,ϕ),...
Variational methods in nonlinear problems