AN ITERATIVE SOLUTION OF A UNIFORMLY CONTINUOUS ACCRETIVE OPERATOR EQUATION

Niyati Gurudwan, B. K. Sharma

Abstract


A strong convergence theorem for the zero of a uniformly continuous accretive operator in a real normed space is proved using the iteration formula

x_{n+1} = x_n - \lambda_n \alpha_n Ax_n - \lambda_n \theta_n (x_n - x_1), for n >=1

where {\alpha_n}_{n=1}^{\infty}, {\lambda_n}_{n=1}^{\infty} and {\theat_n}_{n=1}^{\infty} are real sequences in (0, 1 satisfying certain conditions given by Chidume and Zegeye [9]. Similar result for uniformly continuous pseudocontractive map is also proved. Our result modifies the convergence results of Chidume and Ofoedu [7] and many others.

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ISSN: 1229-1595 (Print), 2466-0973 (Online)