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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 164851, 8 pages
http://dx.doi.org/10.1155/2013/164851
Research Article

Convexity of Solutions for an Iterative Equation in Banach Spaces

1Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, Sichuan 641100, China
2College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641100, China

Received 18 March 2013; Accepted 2 August 2013

Academic Editor: Abdelghani Bellouquid

Copyright © 2013 Xiaobing Gong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By applying Schauder's fixed point theorem we investigate the existence of increasing (decreasing) solutions of the iterative equation and further give conditions under which those solutions are convex or concave. As corollaries we obtain results on iterative equation in Banach spaces, where .