On the proximal point algorithm and its Halpern-type variant for generalized monotone operators in Hilbert space

Abstract In a recent paper, Bauschke et al. study $$\rho $$ ρ -comonotonicity as generalized notion of monotonicity set-valued operators A in Hilbert space and characterize this condition on terms the averagedness its resolvent $$J_A.$$ J A . note we show that result makes it possible to adapt many proofs properties proximal point algorithm PPA strongly convergent Halpern-type variant HPPA more general class operators. This also applies quantitative results rates convergence or metastability (in sense T. Tao). E.g. using approach get simple proof for boundedly compact case -comonotone obtain an effective rate metastability. If has modulus regularity w.r.t. $$zer\, A$$ z e r some zero even without any compactness assumption. We operators, prove strong (without assumption) give