Abstract
This paper is devoted to prove the existence of continuous solutions for a nonlinear integral equation. Our existence theorem extends in a broad sense the analogous one obtained by L.T.P. Ngoc and N.T. Long. To this aim we first prove new variants of the Krasnosel’skii–Sadowskii and of the Krasnosel’skii–Däher fixed point theorems in Hausdorff locally convex topological vector spaces. These hybrid theorems improve some recently obtained results. Moreover a fixed point theorem for a multimap defined on a cartesian product subset of a Banach space is stated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Basoc I., Cardinali T.: A hybrid nonlinear alternative theorem and some hybrid fixed point theorems for multimaps. J. Fixed Point Theory Appl. 17, 413–424 (2015)
Burton T.A., Kirk C.: A fixed point theorem of Krasnoselskii–Schaefer type. Math. Nachr. 189, 23–31 (1998)
Cardinali, T., O’Regan, D., Rubbioni, P.: Mönch sets and fixed point theorems for multimaps in locally convex topological vector spaces. Fixed Point Theory (in press)
Cardinali T., Papalini F.: Fixed point theorems for multifunctions in topological vector spaces. J. Math. Anal. Appl. 186, 769–777 (1994)
Cardinali T., Rubbioni P.: Countably condensing multimaps and fixed points. Electron. J. Qual. Theory Differ. Equ. 83, 1–9 (2012)
Denkowski Z., Migorski S., Papageorgiou N.S.: An Introduction to Nonlinear Analysis, Theory. Kluwer Academic/Plenum Publishers, NY (2003)
Dhage, B.C.: Multi-valued mappings and fixed points I. Nonlinear Funct. Anal. Appl. 10(3), 359–378 (2005)
Hu S.C., Papageorgiou N.S.: Handbook of Multivalued Analysis, Vol. I: Theory. Springer, Berlin (1997)
Köthe G.: Topological Vector Spaces (I). Springer, Berlin (1969)
Krasnosel’skii M.A.: Some problems of nonlinear analysis. Am. Math. Soc. Trans. 10(2), 345–409 (1958)
Ngoc, L.T.P., Long, N.T.: On A fixed point theorem of Krasnosel’skii type and application to integral equations. Fixed Point Theory Appl. (2006). doi:10.1155/FPTA/2006/30847
O’Regan D.: Fixed-point theory for the sum of two operators. Appl. Math. Lett. 9(1), 1–8 (1996)
Petrusel A.: Multivalued operators and fixed points. Pure Math. Appl. (PU.M.A.) 9, 165–170 (1998)
Przeslawski K., Rybinski L.E.: Michael selection theorem under weak lower semicontinuity assumption. Proc. Am. Math. Soc. 109, 537–543 (1990)
Rybinski L.E.: An application of the continuous selection theorem to the study of the fixed points of multivalued mappings. J. Math. Anal. Appl. 153, 391–396 (1990)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Biondini, M., Cardinali, T. Existence of Solutions for a Nonlinear Integral Equation via a Hybrid Fixed Point Theorem. Results Math 71, 1259–1276 (2017). https://doi.org/10.1007/s00025-016-0552-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-016-0552-9