Caristi-Type Fixed-Point Theorems in the Framework w-Distances

The aim of this paper is to generalize Caristi’s theorem, Bollenbacher and Hicks’ theorem, and also Hicks and Rhoades’ theorem by substituting the continuity assumption with relatively weaker conditions of k-continuity or (C; k) condition in a complete metric space with a w-distance. Another proof for Caristi’s theorem using Zorn’s lemma will be given. Some examples will confirm the novelty and usefulness of our results.