Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
30 January 2020 |
14 February 2020 |
10 March 2020 |
Abstract: In this work, we define a metric structure d in a set E endowed with a binary relational system and we prove that if the generalized metric space (E, d) has a compact and normal structure then every non expansive mapping has a fixed point. Our proof differs from that given by the authors in [7], since it adapt a constructive lemma due to Gillespie and Williams [3]. We obtain Tarski’s fixed point theorem as a corollary. We also establish DeMarr’s type fixed point theorem for an arbitrary family of symmetric Banach operator pairs and we give an illustration of the latter result via an example.
