Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative method in Banach spaces

Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, presented here for the first time, we introduce and study the class of {\it enriched nonexpansive mappings} in Hilbert spaces. In order to approximate the fixed points of enriched nonexpansive mappings we use the Krasnoselskij iteration for which we prove strong and weak convergence theorems. Examples to illustrate the richness of the new class of contractive mappings are also given. Our results in this paper extend some classical convergence theorems established by Browder and Petryshyn in [Browder, F. …

Krasnoselskij-type algorithms for variational inequality problems and fixed point problems in Banach spaces

Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in the setting of a Banach space. The main tool used in the investigations is to work with the averaged operator $T_λ$ instead of the original operator $T$. The effectiveness of the new results thus derived is illustrated by appropriate examples. An application of the strong convergence theorems to solving a variational inequality is also presented.

关于b-富集非扩张映射的注记

Remarks on b-enriched nonexpansive mappings

该研究针对文献中提出的富集非扩张映射概念展开分析，指出其与经典非扩张映射概念重合，需重新审视，为度量不动点理论的相关文献研究提供参考并指明后续澄清方向。

Existence and data dependence results for the fixed points of multivalued mappings

We introduce multivalued Górnicki mapping and various new types of multivalued enriched contractive mappings, viz., multivalued enriched Kannan mapping, multivalued enriched Chatterjea mapping, and multivalued enriched Cirić-Reich-Rus mapping. Then we establish some existence results for the fixed points of these multivalued contractive type mappings using the fixed point property of the average operator of the mappings. Furthermore, we present some data dependence results for the fixed points of mentioned classes of mappings.