Let a non-empty, bounded, closed and convex subset of a Banach space , and denote by the -sum of . In the present paper, by using the degree of nondensifiability (DND), we introduce the class of --DND-contraction maps and prove that if then there is some with . Our result, in the specified framework, generalizes other fixed point results for the so called generalized -contraction and even other existing fixed point result based on the DND. Also, we derive a new Krasnosel’skiĭ-type fixed point result.
Cite this article
Gonzalo García, A fixed point result for mappings on the -sum of a closed and convex set based on the degree of nondensifiability. Port. Math. 79 (2022), no. 1/2, pp. 199–210DOI 10.4171/PM/2081