On dynamical systems and fixed point theory in Eilenberg-Jachymski spaces

We introduce the sets of periodic, recurrent, ω-limit and nonwandering points for a selfmap defined on a nonempty set endowed with an Eilenberg-Jachymski collection. Then, under some appropriate conditions, we show that these sets all coincide. Moreover, we establish fixed and periodic point theorems for a new class of φ-contractive mappings in ψ-dislocated metric spaces, and generalize some results obtained by Edelstein, Matkowski and Bessenyei-Páles.