Document Type
Report
Source Publication Title
Technical Report 29
Abstract
In a recent paper, Petryshyn and Williamson [4] investigated the convergence of successive approximations of quasi- nonexpansive mappings in a Banach space. This paper contains an outline, in chronological order, of the main results concerning the convergence of iteration method and consequently includes a number of references. Perov and Kibenko [3] employed generalized Banach spaces to extend contraction mapping principal and to show the flexibility of such an approach in applications. See also Bernfeld and Lakshmikantham [1]. More recently, Eisenfeld and Lakshmikantham [5,6] proved some fixed point theorems in abstract cones which extend and generalize many known results. In this paper, we extend some main results of [4] to cone-valued metric spaces. In Sections 2 and 3, we give needed definitions and properties of k-metric spaces and in Section 4, we prove our main results. For convenience and for future use, we have given more details than necessary.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
7-1-1975
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Williams, B. B. and Bolen, J. C., "On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones" (1975). Mathematics Technical Papers. 310.
https://mavmatrix.uta.edu/math_technicalpapers/310