Convergence Theorems for Strongly Pseudo-contractive and Strongly Accretive Maps

Suppose E is an arbitrary real Banach space and K is a nonempty closed convex and bounded subset of E. Suppose T: KªK is a uniformly continuous strong pseudo-contraction with constant kg 0, 1.. Suppose an4, bn4, cn4, aXn4, bXn4, and cXn4are sequences in 0, 1. satisfying the following conditions: i. anqbnqcns1 saXnqbXnqcXn;integers nG0; ii. lim bnslim bXnslim cXns0; iii. Sbns`; iv. Scn-`. For arbitrary x0, u0, ¨0gK, define the sequence xn4`ns0 iteratively by xnq1sanxnqbnTynqcnun; ynsaXnxnqbXnTxnqcXn¨n, nG0, where un4, ¨n4are arbitrary sequences in K. Then xn4converges strongly to the unique fixed point of T. Related results deal with the iterative solutions of nonlinear equations involving set-valued, strongly accretive operators.