We originate some existence results on periodic and fixed point using generalized (ψ ᵒ φ)- contractions and generalized (ψ, φ)-contractive mappings with weaker Meir-Keeler function in the setup of a complete generalized metric space in sense of Branciari without Hausdorff assumption. Our results generalize the results of several well-known comparable results in the literature. To illustrate our results, we conclude the paper with some examples. © 2016, University of Nis. All rights reserved.