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La clase de los operadores finalmente compactos en el sentido de Sadovski contiene las clases de operadores condensantes, compactos y contractivos. Se deducen teoremas de punto fijo para operadores estocásticos finalmente compactos superiormente semicontinuos, usando el grado de Leray-Schauder y sus generalizaciones a operadores determinísticos., Ultimately compact operators in the sense of Sadovski contain the classes of condensing, of compact and contractive operators. Fixed-point theorems are derived for upper semicontinuous ultimately compact stochastic operators using the Leray-Schauder degree and its generalizations for deterministic operators

Tipo de documento: Artículo - Article

Palabras clave: class of operators; sense Sadovsky, theorems, fixed points stochastic operators; degree of Leray-Schauder; deterministic operators, clase de los operadores, sentido de Sadovski, teoremas, puntos fijos, operadores estocásticos, grado de Leray-Schauder, operadores determinísticos





Fuente: http://www.bdigital.unal.edu.co


Introducción



Rev~ta Cotomb~na de Mat~ca6 Vat.
XVI (1982) pag~.
95 - 114 RANDOM FIXED ULTIMATELY POINT COMPACT THEOREMS FOR OPERATORS by Gerhard SCHLEINKOFER * RESUMEN. La clase de los operadores finalmente compactos en el sentido de Sadovski contiene las clases de operadores condensantes, compactos y contractivos.
Se deducen teoremas de punto fijo para operadores estocasticos finalmente compactos superiormente semicontinuos, usando el grado de Leray-Schauder y sus generalizaciones a operadores determinlsticos. ABSTRACT. Ultimately compact operators in the sense of Sadovski contain the classes of condensing, of compact and contractive operators.
Fixed-point theorems are derived for upper semicontinuous ultimately compact stochastic operators using the Leray-Schauder degree and its generalizations for deterministic operators. Introduction. An appropriate starting point for stoch- astic operators is the abstract fixed-point formulation of exis- * This work is partially supported by the Deutscher Akademischer Austauschdienst, D-5300 Bonn. 95 tence problems for differential equations under Caratheodoryconditions (see Coddington, Levinson [4] and Engl [7] ).
The corresponding problems for multivalued differential equations lead to the consideration of random fixed-points for stochastic multifunctions T( ,·):wxX 2X, where X is a separable Banach space. If (w,) is a continuous operator with respect to the Haus-i9r}~fdistance in 2X for each w €.
W, the problem has been solved by Kannan and Salehi [11J and by Engl [7, Theorem 6].
Their theorem says that T always has a random fixed-point if the corresponding deterministic operator T(w,) has a fixed-point for each we:.W. However, most fixed-point theorems and the Leray-Schauder degree for multifunctions refer to the larger class of upper semicontinuous (u.s.c.) multifunctions. The main difficulty that arises here is that generally the operator T(·,·) is not jointly measurable on WXX. For compact u.s.c.
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