On Ekeland Variational Principle in Asymmetric b-Metric Spaces

This paper extends the Ekeland Variational Principle (EVP) to the setting of asymmetric b-metric spaces,
which generalize both asymmetric metric and b-metric spaces. By distinguishing forward, backward and bi-
completeness, we establish corresponding forward, backward and bi-complete version of EVP. Examples are
provided to demonstrate that forward and backward principles may yield different minimizers while the bi-complete
EVP reduces to the classical EVP when symmetry holds. As an application, we obtain a forward and backward
Cartisi-type fixed point theorem. These results broaden the scope of EVP and offer a new tools for optimization
and fixed-point theory in asymmetric frameworks.