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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.

A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper.

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo, s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash, Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam&ndash, Hyers stability of the fixed point problem. An example is also given to sustain the presented results.