In this paper, new classes of rational Geraghty contractive mappings in the setup of b-metric spaces are introduced. Moreover, the existence of some fixed point for such mappings in ordered b-metric spaces are investigated. Also, some examples are provided to illustrate the results presented herein. Finally, an application of the main result is given.for all x, y, z ∈ X.In this case, the pair (X, d) is called a b-metric space.The following example (corrected from []) illustrates that a b-metric need not be a continuous function.if one of m, n is even and the other is even or ∞, , if one of m, n is odd and the other is odd (and m = n) or ∞, , otherwise.

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In this note, we show that under certain assumptions the scalar Riccati differential equationperiodic coefficients admits at least one periodic solution. Also, we give two illustrative examples in order to indicate the validity of the assumptions. The research of M.R. Pournaki and A. Razani was in part supported by a grant from IPM (Nos. 86200111 and 86340022).