Weak and strong convergence theorems for enriched strictly pseudocontractive operators in Hilbert spaces

英文摘要：

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of fixed points of nonlinear mappings in Hilbert space}, J. Math. Anal. Appl. {\bf 20} (1967), 197--228] and Theorem 3.1 in [Marino, G., Xu, H.-K., {\it Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces}, J. Math. Anal. Appl. {\bf 329} (2007), no. 1, 336--346], from the class of strictly pseudocontractive mappings to that of enriched strictly pseudocontractive mappings and thus include many other important related results from literature as particular cases.