Skip to content


  • Research Article
  • Open Access

Existence and Data Dependence of Fixed Points and Strict Fixed Points for Contractive-Type Multivalued Operators

Fixed Point Theory and Applications20072007:034248

  • Received: 21 October 2006
  • Accepted: 2 December 2006
  • Published:


The purpose of this paper is to present several existence and data dependence results of the fixed points of some multivalued generalized contractions in complete metric spaces. As for application, a continuation result is given.


  • Differential Geometry
  • Computational Biology
  • Data Dependence
  • Dependence Result
  • Generalize Contraction


Authors’ Affiliations

Department of Business, Faculty of Business, Babeş-Bolyai University Cluj-Napoca, Horea 7, Cluj-Napoca, 400174, Romania
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu 1, Cluj-Napoca, 400084, Romania


  1. Rus IA, Petruşel A, Petruşel G: Fixed Point Theory: 1950–2000. Romanian Contributions. House of the Book of Science, Cluj-Napoca, Romania; 2002:xiv+308.Google Scholar
  2. Rus IA, Petruşel A, Sîntămărian A: Data dependence of the fixed point set of some multivalued weakly Picard operators. Nonlinear Analysis 2003,52(8):1947–1959. 10.1016/S0362-546X(02)00288-2MATHMathSciNetView ArticleGoogle Scholar
  3. Reich S: Fixed points of contractive functions. Bollettino della Unione Matematica Italiana. Serie IV 1972, 5: 26–42.MATHGoogle Scholar
  4. Petruşel A: Multivalued weakly Picard operators and applications. Scientiae Mathematicae Japonicae 2004,59(1):169–202.MATHMathSciNetGoogle Scholar
  5. Feng Y, Liu S: Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings. Journal of Mathematical Analysis and Applications 2006,317(1):103–112. 10.1016/j.jmaa.2005.12.004MATHMathSciNetView ArticleGoogle Scholar
  6. Ćirić LB: Generalized contractions and fixed-point theorems. Publications de l'Institut Mathématique. Nouvelle Série 1971, 12(26): 19–26.Google Scholar
  7. Covitz H, Nadler SB Jr.: Multi-valued contraction mappings in generalized metric spaces. Israel Journal of Mathematics 1970, 8: 5–11. 10.1007/BF02771543MATHMathSciNetView ArticleGoogle Scholar
  8. Nadler SB Jr.: Multi-valued contraction mappings. Pacific Journal of Mathematics 1969, 30: 475–488.MATHMathSciNetView ArticleGoogle Scholar
  9. Petruşel A: Generalized multivalued contractions. Nonlinear Analysis 2001,47(1):649–659. 10.1016/S0362-546X(01)00209-7MATHMathSciNetView ArticleGoogle Scholar
  10. Reich S: A fixed point theorem for locally contractive multi-valued functions. Revue Roumaine de Mathématiques Pures et Appliquées 1972, 17: 569–572.MATHGoogle Scholar
  11. Rus IA: Fixed point theorems for multi-valued mappings in complete metric spaces. Mathematica Japonica 1975, 20: 21–24. special issueMathSciNetGoogle Scholar
  12. Rus IA: Generalized Contractions and Applications. Cluj University Press, Cluj-Napoca, Romania; 2001:198.MATHGoogle Scholar
  13. Frigon M, Granas A: Résultats du type de Leray-Schauder pour des contractions multivoques. Topological Methods in Nonlinear Analysis 1994,4(1):197–208.MATHMathSciNetGoogle Scholar
  14. Agarwal RP, Dshalalow J, O'Regan D: Fixed point and homotopy results for generalized contractive maps of Reich type. Applicable Analysis 2003,82(4):329–350. 10.1080/0003681031000098470MATHMathSciNetView ArticleGoogle Scholar
  15. Chiş A, Precup R: Continuation theory for general contractions in gauge spaces. Fixed Point Theory and Applications 2004,2004(3):173–185. 10.1155/S1687182004403027MATHGoogle Scholar


© C. Chifu and G. Petruşel. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.