From convex contraction to Banach contraction
DOI:
https://doi.org/10.12775/TMNA.2026.009Keywords
Convex contraction, Banach contraction, Picard iterative sequenceAbstract
The purpose of this paper is to show that a convex contraction of arbitrary order in the setting of a complete metric space is indeed a Banach contraction on another complete metric space. In that way, existence and uniqueness of a fixed point for the class of convex contractions will be a direct corollary of the Banach contraction principle. We will consider previously given examples of convex contractions which are not contractions and discuss on the iterative sequences and their convergence through some numerical examples. Additionally, we will comment on the correspondence between convex and Banach contractions in different settings, with some open questions for further research.References
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