No abstract

The purpose of this paper is to present a fixed point theory for multivalued -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-toset operatorial equations and fractal operators. Our results generalize some recent theorems given in Petruşel and Rus (The theory of a metric fixed point theorem for multivalued operators,

The purpose of this paper is to study the solution set of the functional inclusion of n-th order of the following form:where the function G : X × Y n −→ P cl,cv (Y ) and f 1 , f 2 , ..., f n : X −→ X are given. The approach is based on some fixed point theorems for multivalued operators, satisfying the nonlinear contraction condition, see [

Using the weakly Picard operator technique, we will present some Ulam-Hyers stability results for some partial differential equations.