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In this paper, we establish some fixed point results for <em>α</em>-dominated mappings fulfilling new generalized locally Ćirić type rational contraction conditions in complete rectangular <em>b</em>-metric space. As an application, we establish the existence of fixed point of $\preceq $-dominated mappings in an ordered complete rectangular <em>b</em>-metric space. The notion of graph dominated mappings is introduced. Fixed point results with graphic contractions for such mappings are established.