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In this paper, we obtain some fixed point theorems for admissible mappings in b-metric spaces. Some useful examples are given to illustrate the facts. We also discuss an application to a nonlinear quadratic integral equation. Our results complement, extend and generalize a number of fixed point theorems including the well-known Geraghty [M. A. Geraghty, Proc. Amer. Math. Soc., 40 (1973), 604-608]

<p>We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappingss in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed.</p>

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