Some results on a general iterative method for <it>k</it>-strictly pseudo-contractive mappings

Abstract Let H be a Hilbert space, C be a closed convex subset of H such that C &#177; C &#8834; C, and T : C &#8594; H be a k-strictly pseudo-contractive mapping with F(T) &#8800; &#8709; for some 0 &#8804; k &lt; 1. Let F : C &#8594; C be a &#954;-Lipschitzian and &#951;-strongly monotone operator with &#954; &gt; 0 and &#951; &gt; 0 and f : C &#8594; C be a contraction with the contractive constant &#945; &#8712; (0, 1). Let , and &#964; &lt; 1. Let {&#945;n } and {&#946;n } be sequences in (0, 1). It is proved that under appropriate control conditions on {&#945;n } and {&#946;n }, the sequence {xn } generated by the iterative scheme x n+1 = &#945; n &#947;f(x n ) + &#946; n x n + ((1 - &#946; n )I - &#945; n &#956;F)P C Sx n , where S : C &#8594; H is a mapping defined by Sx = kx + (1 - k)Tx and PC is the metric projection of H onto C, converges strongly to q &#8712; F(T), which solves the variational inequality &#9001;&#956;Fq - &#947;f(q), q - p&#9002; &#8804; 0 for p &#8712; F(T). MSC: 47H09, 47H05, 47H10, 47J25, 49M05