Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the Lebesgue space

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3283-3293

  Banaś, Józef ^a  

^a UNIVERSITY OF RZESZÓW   (Poland)

Author keywords

Demicontinuity; Measure of weak noncompactness; Urysohn integral equation; Weak continuity; Weak sequential continuity

Indexed keywords

EID: 0042546240     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00157-5     Document Type: Article

References (21)

1. APPELL J. & DE PASCALE E., Su alcuni parametri connessi con la misura di non compattezza di Hausdorff in spazi di funzioni misurabili, Boll. Un. Mat. Ital (6), 3-B, 497-515 (1984).
2. APPELL J. & ZABREJKO P.P., Nonlinear Superposition Operators, Cambridge Tracks in Mathematics 95, Camb. Univ. Press (1990).
3. ARINO O., GAUTIER S. & PENOT J.P., A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkc. Ekvac. 27, 273-279 (1984).
4. BANAŚ J., On the superposition operator and integrable solutions of some functional equations, Nonlin. Analysis T.M.A. 12, 777-784 (1988).
5. BANAŚ J, Integrable solutions of Hammerstein and Urysohn integral equations, J. Austral. Math. Soc. 46, 61-68 (1989).
6. BANAŚ J. & GOEBEL K., Measures of Noncompactness in Banach Spaces, Lect. Notes in Pure and Applied Math. 60, M. Dekker, New York and Basel (1980).
7. CASTAING C., Une nouvelle extension du théorème de Dragoni-Scorza, C.R. Acad. Sci., Paris, Sér. A 271, 396-398 (1970).
8. DE BLASI F.S., On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. R.S. Roum. 21, 259-262 (1977).
9. DIEUDONNÉ J., Sur les espaces de Köthe, J. Analyse Math. I, 81-115 (1951).
10. DUNFORD N. & PETTIS B.J., Linear operators on summable functions, Trans. Amer. Math. Soc. 47, 323-392 (1940).
11. DUNFORD N. & SCHWARTZ J., Linear Operators I, Int. Publ., Leyden (1963).
12. EMMANUELE G., Measures of weak noncompactness and fixed point theorems, Bull. Math. Soc. Sci. Math. R.S. Roum. 25, 353-358 (1981).
13. EMMANUELE G., Integrable solutions of a functional-integral equation, J. Integral Equations 4, 89-94 (1992).
14. KRASNOSEL'SKII M.A., it On the continuity of the operator Fu(cursive Greek chi) = f(cursive Greek chi, u(cursive Greek chi)), Dokl. Akad. Nauk. SSSR 77, 185-189 (1951).
15. KRASNOSEL'SKII M.A., ZABREJKO P.P., PUSTYL'NIK J.I. & SOBOLEVSKII P.J., Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden (1976).
16. KUCZMA M., Functional Equations in a Single Variable, Monografie Mat. 46, Warszawa (1968).
17. MATKOWSKI J., Integrable solutions of functional equations, Dissert. Math. 127 (1975).
18. SCORZA DRAGONI G., Un teorema sulle funzioni continue rispetto ad une e misurabili rispetto ad un'altra variable, Rend. Sem. Mat. Univ. Padova 17, 102-106 (1948).
19. SHRAGIN V.I., On the weak continuity of the Nemytskii operator, Uchen. Zap. Mosk. Obl. Ped. Inst. 57, 73-79 (1957).
20. VAINBERG M.M., Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, Wiley (1973).
21. ZABREJKO P.P., KOSHELEV A.I., KRASNOSEL'SKII M.A., MIKHLIN S.G., RAKOVSHCHIK L.S. & STECENKO V.J., Integral Equations, Noordhoff, Leyden (1975).