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Samet et al. in (Nonlinear Anal. 75:2154-2165, 2012) introduced the concepts of α-ψ-contractive type mappings and α-admissible mappings in metric spaces. The purpose of this paper is to present a new class of almost contractive mappings called almost generalized \((\alpha\mbox{-}\psi\mbox{-}\varphi\mbox {-}\theta)\)-contractive mappings and to establish some fixed and common fixed point results for this class of mappings in complete ordered b-metric spaces. Our results improve and generalize several known results from the current literature and its extension. Moreover, an application to integral equations is given here to illustrate the usability of the obtained results.

Fixed points of admissible almost contractive type mappings on b-metric spaces with an application to quadratic integral equations