The purpose of this paper is to introduce the class of enriched multivalued contraction mappings. Both single-valued and multivalued enriched contractions are defined by means of symmetric inequalities. Our main result extends and generalizes the recent result of Berinde and Păcurar (Approximating fixed points of enriched contractions in Banach spaces, Journal of Fixed Point Theory and Applications, 22 (2), 1–10, 2020). We also study a data dependence problem of the fixed point set and Ulam–Hyers stability of the fixed point problem for enriched multivalued contraction mappings. Applications of the results obtained to the problem of the existence of a solution of differential inclusions and dynamic programming are presented.
The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.
The purpose of this paper is to introduce the class of (a,b,c)-modified
enriched Kannan pair of mappings (T,S) in the setting of Banach space that
includes enriched Kannan mappings, contraction and nonexpansive mappings and
some other mappings. Some examples are presented to support the concepts
introduced herein. We establish the existence of common fixed point of the
such pair. We also show that the common fixed point problem studied herein
is well posed. A convergence theorem for the Krasnoselskij iteration is used
to approximate fixed points of the (a,b,c)-modified enriched Kannan pair.
As an application of the results proved in this paper, the existence of a
solution of integral equations is established. The presented results
improve, unify and generalize many known results in the literature.
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