Entropy points of continuous maps with the sensitivity and the shadowing property

We give some sufficient conditions that a point can be approximated by an entropy point in terms of the sensitivity and the shadowing property. More precisely, we prove that for a continuous self-map f of a compact metric space X and a closed f  -invariant subset S⊂XS⊂X, if eventually sensitive points of f|Sf|S are dense in S, then any point of S can be approximated by an entropy point with an accuracy corresponding to that of the shadowing. Moreover, its homeomorphisms version and two corollaries are proved.