Fixed point theory for multivalued φ-contractions

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,

Dynamics and Ulam Stability for Fractionalq-Difference Inclusions via Picard Operators Theory

“…Theorem 2.7. [20] Let Q be a multivalued mapping from a complete metric space (M, δ) to P cl (M), and λ ∈ S.…”

A study of some properties of an n-order functional inclusion

“…The approach is based on some recent results (see Lazȃr [1]) concerning the fixed point problem for multivalued operators, given in terms of multivalued ϕ-contractions. For related results concerning multivalued nonlinear contractions, see [2], [5], [6] and [7].…”