|
|
Fixed point theory for multivalued φ-contractionsKeywords: successive approximations , multivalued operator , Picard operator , weakly Picard operator , fixed point , strict fixed point , periodic point , strict periodic point , multivalued weakly Picard operator , multivalued Picard operator , data dependence , fractal operator , limit shadowing , set-to-set operator , Ulam-Hyers stability , sequence of operators Abstract: The purpose of this paper is to present a fixed point theory for multivalued φ-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
|
