Approximating fixed points of strongly pseudocontractive mappings by a new iteration method

摘要

In this article we investigate the convergence of the iterative process defined by x{sub}(n+1) =(t{sub}n){sup}(1)T(t{sub}n){sup}(2)T{…T(((t{sub}n){sup}(k))Tx{sub}n + (1-((t{sub}n){sup}(k)))x{sub}n+(u{sub}n){sup}(k))+…}+(1-((t{sub}n){sup}(2)))x{sub}n+(u{sub}n){sup}(2))+(1-((t{sub}n){sup}(1)))x{sub}n+(u{sub}n){sup}(1) x{sub}0∈X, n=1,2,3…, for strongly pseudocontractive mappings, where ((u{sub}n){sup}(i)),i=(1,k){top}-, are k sequences in a real Banach space X and ((t{sub}n){sup}(i)),i=(1,k){top}- are k real sequences in the interval [0, 1]. Also, we investigate a class of difference inequalities that often appears in the investigation of the iterative process.