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

2019/09/05 by Vasile Berinde, Berinde, Vasile, Mădălina Pačurar +1
Mathematics · #47H09 #47H10 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1909.03494

openalex publication_date 2019/09/05 · openalex created_date 2019/09/12 · openalex updated_date 2026/07/28

Abstract

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., \it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math. \bf 35 (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and prove general fixed point theorems for such contractions in the setting of a Banach space. Examples to illustrate the richness of the new class of contractions and the relationship between enriched Banach contractions, enriched Kannan contractions and enriched Kannan contractions are also given.

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