| Summary: | In this manuscript, we consider some hybrid contractions that merge linear and nonlinear contractions in the abstract spaces induced by the Branciari distance and the Branciari <i>b</i>-distance. More precisely, we introduce the notion of a <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>c</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-weight type <inline-formula> <math display="inline"> <semantics> <mi>ψ</mi> </semantics> </math> </inline-formula>-contraction in the setting of Branciari distance spaces and the concept of a <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>c</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-weight type contraction in Branciari <i>b</i>-distance spaces. We investigate the existence of a fixed point of such operators in Branciari type distance spaces and illustrate some examples to show that the presented results are genuine in the literature.
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