Fixed point theorems for condensing multivalued mappings under weak topology features

Fixed Point Theory

Volumn 12, Issue 2, 2011, Pages 247-254

  Agarwal, Ravi P ^a,b   O'Regan, Donal ^c   Taoudi, Mohamed Aziz ^d,e  

^a Florida Institute of Technology ^*  (United States)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^c NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^d CADI AYYAD UNIVERSITY   (Morocco)

^e Centre Universitaire Kalaa des Sraghnas   (Morocco)

Author keywords

Krasnosel'skii's fixed point theorem; Leray Schauder's fixed point theorem; Measure of weak noncompactness; Multivalued maps; Sadovskii's fixed point theorem; Weakly condensing

Indexed keywords

EID: 80055068246     PISSN: 15835022     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. R.P. Agarwal, D. O'Regan, M.A. Taoudi, Browder-Krasnoselskii type fixed point theorems in Banach spaces, Fixed Point Theory Appl. 2010(2010), Article ID 243716, 20 pp.
2. R.P. Agarwal, D. O'Regan, Fixed point theory for k-CAR sets, J. Math. Anal. Appl., 251(2000), no. 1, 13-27.
3. R.P. Agarwal, D. O'Regan, Fixed point theory for weakly sequentially upper-semicontinuous maps with applications to differential inclusions, Nonlinear Oscillations, 5(2002), no. 3, 277-286.
4. O. Arino, S. Gautier and J. P. Penot, A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkc. Ekvac., 27(1984), 273-279.
5. J. Banas, J. Rivero, On measures of weak noncompactness, Ann. Mat. Pura Appl., 151(1988), 213-224.
6. D. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20(1969), 458-464.
7. F.S. De Blasi, On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. Roum., 21(1977), 259-262.
8. N. Dunford, J.T. Schwartz, Linear Operators, Part I: General Theory, Interscience Publishers, New York, 1958.
9. R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
10. K. Floret, Weakly compact sets, Lecture Notes in Mathematics, 801, Springer, Berlin, 1980.
11. J. Garcia-Falset, Existence of fixed points and measure of weak noncompactness, Nonlinear Anal., 71(2009), 2625-2633.
12. G.J.O. Jameson, An elementary proof of the Arens and Borsuk extension theorems, J. London Math. Soc., 14(1976), 364-368.
13. I. Kubiaczyk, On a fixed point theorem for weakly sequentially continuous mapping, Discussiones Math.-Diff. Incl., 15(1995), 15-20.
14. D. O'Regan, Fixed point theory for weakly contractive maps with applications to operator inclusions in Banach spaces relative to the weak topology, Zeitschrift für Analysis und ihre Anwendungen, 17(1998), 282-296.
15. D. O'Regan, Fixed point theorems for weakly sequentially closed maps, Arch. Math., 36(2000), no. 1, 61-70.
16. D. O'Regan, M.A. Taoudi, Fixed point theorems for the sum of two weakly sequentially continuous mappings, Nonlinear Anal., 73(2010), no. 2, 283-289.
17. E. Zeidler, Nonlinear Functional Analysis and its Applications, I: Fixed Point Theorems, Springer-Verlag, New York, 1986.