Common fixed points for two implicit contractive mappings of integral type on ordered metric spaces

Abstract

In this paper, we introduce three real functional classes $\mathcal{C^{*}}$ and $\Phi_{c}^*$ and $\Phi_{u}^*$, and discuss the existence problems of common fixed points for two mappings of integral type with implicit contractive conditions determined by $\mathcal{C^{*}}$ and $\Phi_{c}^*$ and $\Phi_{u}^*$ on non-complete ordered metric spaces and give more general results.