Istr\u{a}\c{t}escu type contractions on new extended $b$-metric spaces

Abstract

This paper investigates mappings with Istr\u{a}\c{t}escu type
contractive properties within the framework of new extended
$b$-metric spaces. Various generalized contractive operators are
defined, including those of order $2$, two-sided, type $2$, and
\'{C}iri\'{c}-convex contractions. The study establishes several
fixed point theorems for these mappings under specific conditions,
such as orbital continuity or the boundedness of the function
involved in the structure of the new extended $b$-metric space.
These results extend previous findings in the literature.