The existence of anti-periodic solutions is studied for a second order difference inclusion associated with a maximal monotone operator in Hilbert spaces. It is the discrete analogue of a well-studied class of differential equations.
Let be domain in a complex Banach space , and let be a pseudometric assigned to by a Schwarz-Pick system. In the first section of the paper we establish several criteria for a mapping to be a generator of a -nonexpansive semigroup on in terms of its nonlinear resolvent. In the second section we let be a complex Hilbert space, the open unit ball of , and the hyperbolic metric on . We introduce the notion of a -monotone mapping and obtain simple characterizations of generators...
Let X be a real Banach space and G ⊂ X open and bounded. Assume that one of the following conditions is satisfied: (i) X* is uniformly convex and T:Ḡ→ X is demicontinuous and accretive; (ii) T:Ḡ→ X is continuous and accretive; (iii) T:X ⊃ D(T)→ X is m-accretive and Ḡ ⊂ D(T). Assume, further, that M ⊂ X is pathwise connected and such that M ∩ TG ≠ ∅ and . Then . If, moreover, Case (i) or (ii) holds and T is of type , or Case (iii) holds and T is of type , then M ⊂ TG. Various results of Morales,...
We extend Zajíček’s theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a -cone supported set.
Les solutions d’équations d’évolution où est un opérateur maximal monotone d’un espace de Hilbert , et sont étudiées dans le cas général en introduisant une notion de solution faible. Des résultats particuliers sont donnés lorsque est de dimension finie ou plus généralement lorsque l’intérieur de est non vide.
Some properties of monotone type multivalued operators including accretive operators and the duality mapping are studied in connection with the structure of Banach spaces.
In this paper a new class of mappings, known as locally -strongly -accretive mappings, where and have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly -accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally -strongly -accretive mappings by using Caristi-Kirk fixed point theorem. In the sequel, we introduce the notion...
∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone...