Yingying Ju, Chengbo Zhai, Fixed point theorems for $(a,b,\theta)$-enriched contractions, Vol. 2023 (2023), Article ID 15, pp. 1-14

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DOI: 10.23952/jnfa.2023.15

Received December 14, 2022; Accepted April 3, 2023; Published April 25, 2023

Abstract. This paper establishes a new concept for contractive mappings in Banach spaces, called the $(a,b,\theta)$ -enriched contractive mapping. Based upon this new contractive mapping, we obtain three classes of new enriched contractive mappings: $(a,b,k)$ -enriched Kannan mappings, $(a,b,p,q)$ -enriched Ćirić-Reich-Rus mappings, and $(a,b,l)$ -enriched Chatterjea mappings, which extend the corresponding concepts in the literature. We also obtain some new fixed point theorems and Maia type fixed point theorems for these contractive mappings.

How to Cite this Article:
Y. Ju, C. Zhai, Fixed point theorems for $(a,b,\theta)$ -enriched contractions, J. Nonlinear Funct. Anal. 2023 (2023) 15.