On n-ellipse contractive mappings over some extended metric spaces

Abstract

[EN] In this paper, the concept of a mapping contracting axes of an n-ellipse is introduced and its fixed point set has been determined. Investigation of fixed point of mappings over different metric-type spaces is always an interesting study in fixed point theory. We consider a mapping with special characteristic, which is contracting axes of an n-ellipse over two different metric-type structures, Δ -metric space and ℱ -metric space. An enriched version of a mapping contracting axes of an n-ellipse is also introduced, and this class of mappings includes several non-expansive mappings. Moreover, the paper is furnished by some suitable examples that support our results and show that our mapping is distinct from the usual contractive type mappings.