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By using the weaker Meir-Keeler function phi and the triangular alpha-admissible mapping alpha, we introduce the notion of (alpha - phi)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.

Periodic Points of Weaker Meir-Keeler Contractive Mappings on Generalized Quasimetric Spaces