HYBRID STEEPEST ITERATIVE ALGORITHM FOR HIERARCHICAL FIXED POINT PROBLEMS IN UNIFORMLY SMOOTH BANACH SPACES
Abstract
The purpose of this work is to study an iterative method to approximate solutions of Hierarchical fixed point problem involving a nite family of strictly pseudocontractive mappings in uniformly smooth Banach space. The results in this paper are extensions and genelisations of some recent results.References
S. Husain and N. Singh, Hybrid Steepest Iterative Algorithm for a Hierarchical Fixed Point Problem, Fixed Point Theory and Appl. 2017:25, Doi:10.1186/s13663-017-0618-8, (2017).
C. E. Chidume, Geometric properties of Banach Spaces and Nonlinear Iterations, Springer Verlag, Lecture Notes Math. 1965 (2009).
Z. B. Xu, G. F. Roach, Characteristic inequalities of uniformly smooth Banach spaces, J. Math. Anal. Appl. 157 (1991) 189-210.
W. A. Kirk A fixed point theorem for mappings which do not increase distances, The Amer. Math. Monthly, 72 (1965), pp. 1004- 1006.
W. Takahashi, Nonlinear Functional Analysis, Fixed Point Theory and Its Applications, Yokahama, Japan 2000.
W. F. Ames, Numerical Methods for Partial Differential Equations, Third Edit., Academic Press, New York, (1992).