Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 414, Issue 1, Pages 10-20Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2013.12.020
Keywords
Non-Archimedean metric; Cone metric space; Fixed point; Ulam-Hyers stability; Functional equation
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Let (X, p) be a metric space with a K-valued non-Archimedean metric p. In this paper, we prove the existence and approximation of a fixed point for operators F: X -> X satisfying the contractive condition in the form p(F(x), F(y)) <= Q[p(x, y)], where Q : K -> K is an increasing operator. Then, we study the generalized Ulam-Hyers stability of fixed point equations. We next obtain an extension of the Krasnoselskii fixed point theorem for the sum of two operators. Finally, an application to functional equations is given. (C) 2013 Elsevier Inc. All rights reserved.
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