Abstract The aim of this paper is to prove the existence and uniqueness of common fixed points for a pair of $$(\psi -\varphi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo>-</mml:mo> <mml:mi>φ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -weak contractive self-maps in the setting of b -metric spaces satisfying the minimal requirement of weakly compatibility, and other weak commuting properties as compatibility, R -weakly commuting and R -weakly commuting of types ( $$A_T$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>T</mml:mi> </mml:msub> </mml:math> ), ( $$A_S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:math> ) and ( $$A_P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>P</mml:mi> </mml:msub> </mml:math> ). Also, we will analyze the convergence and stability of the Jungck-Noor iterative scheme for this class of pairs of mappings on b -metric spaces endowed with a convex structure.