NEW PROOFS OF SOME FIXED POINT THEOREMS FOR MAPPINGS SATISFYING REICH TYPE CONTRACTIONS IN MODULAR METRIC SPACES

Abstract

Our aim in this paper is to give some new proofs to fixed point theorems due to Abdou [1] for mappings satisfying Reich type contractions in modular metric spaces. We removed the restriction that ω satisfies the ∆₂-type condition imposed on the results of [1]. Furthermore, Lemma 2.6 of [1] which was crucial in the proofs of the results of [1] is not needed in the proofs of our results. Our method of proof is simpler and interesting.