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This also applies to quantitative results on the rates of convergence or metastability (in the sense of T. Tao). E.g. using this approach we get a simple proof for the convergence of the PPA in the boundedly compact case for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\rho $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c1<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-comonotone operators and obtain an effective rate of metastability. If <jats:italic>A<\/jats:italic> has a modulus of regularity w.r.t. <jats:inline-formula><jats:alternatives><jats:tex-math>$$zer\\, A$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>z<\/mml:mi>\n                    <mml:mi>e<\/mml:mi>\n                    <mml:mi>r<\/mml:mi>\n                    <mml:mspace\/>\n                    <mml:mi>A<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> we also get a rate of convergence to some zero of <jats:italic>A<\/jats:italic> even without any compactness assumption. We also study a Halpern-type variant HPPA of the PPA for <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\rho $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03c1<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-comonotone operators, prove its strong convergence (without any compactness or regularity assumption) and give a rate of metastability.<\/jats:p>","DOI":"10.1007\/s11590-021-01738-9","type":"journal-article","created":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T18:03:12Z","timestamp":1618596192000},"page":"611-621","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On the proximal point algorithm and its Halpern-type variant for generalized monotone operators in Hilbert space"],"prefix":"10.1007","volume":"16","author":[{"given":"Ulrich","family":"Kohlenbach","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,16]]},"reference":[{"key":"1738_CR1","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1007\/s11856-017-1511-1","volume":"220","author":"K Aoyama","year":"2017","unstructured":"Aoyama, K., Toyoda, M.: Approximation of zeros of accretive operators in a Banach space. 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