On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space

The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state monotone versions of Theorem 12 in [F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197-228] and Theorem 2.1 in [Berinde, Vasile. Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators, Annals of West University of Timisoara-Mathematics and Computer Science, vol. 56, no. 2, 2018, pp. 13-27], as well as, several related results. Further results, in Hilbert spaces without a partial order, are stated too.