| Summary: | In this paper, by introducing the concept of generalized Ćirić-type weak <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mi>g</mi> </msub> <mo>,</mo> <mi mathvariant="script">R</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">R</mi> </semantics> </math> </inline-formula>. We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.
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