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In this paper, we prove common fixed point theorems for a pair of self-mappings in the framework of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mrow><mi>m</mi><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula>-metric spaces. We also deduce some corollaries of our main result. In order to support our main result, we also set an example.