%0 Journal Article
%T Fixed point theory for multivalued ¦Õ-contractions
%A Laz£¿r Vasile
%J Fixed Point Theory and Applications
%D 2011
%I Springer
%X The purpose of this paper is to present a fixed point theory for multivalued ¦Õ-contractions using the following concepts: fixed points, strict fixed points, periodic points, strict periodic points, multivalued Picard and weakly Picard operators; data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property of a multivalued operator, set-to-set operatorial equations and fractal operators. Our results generalize some recent theorems given in Petru el and Rus (The theory of a metric fixed point theorem for multivalued operators, Proc. Ninth International Conference on Fixed Point Theory and its Applications, Changhua, Taiwan, July 16-22, 2009, 161-175, 2010). 2010 Mathematics Subject Classification 47H10; 54H25; 47H04; 47H14; 37C50; 37C70
%K successive approximations
%K multivalued operator
%K Picard operator
%K weakly Picard operator
%K fixed point
%K strict fixed point
%K periodic point
%K strict periodic point
%K multivalued weakly Picard operator
%K multivalued Picard operator
%K data dependence
%K fractal operator
%K limit shadowing
%K set-to-set operator
%K Ulam-Hyers stability
%K sequence of operators
%U http://www.fixedpointtheoryandapplications.com/content/2011/1/50