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Fixed points and approximately heptic mappings in non-Archimedean normed spaces

Title
Fixed points and approximately heptic mappings in non-Archimedean normed spaces
Author
박춘길
Keywords
heptic functional equation; Hyers-Ulam stability; fixed point method; QUADRATIC FUNCTIONAL-EQUATION; STABILITY; ALGEBRAS
Issue Date
2013-07
Publisher
SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND
Citation
Advances in Difference Equations,2013, p1-10
Abstract
The stability problems concerning group homomorphisms was raised by Ulam [?] in ????and affirmatively answered for Banach spaces by Hyers [?] in the next year. Hyers’ theoremwas generalized by Aoki [?] for additive mappings and by Rassias [?] for linear mappingsby considering an unbounded Cauchy difference. In ????, a generalization of the Rassiastheorem was obtained by G?vruta [?] by replacing the unbounded Cauchy difference by ageneral control function.In ????, Radu [?] proposed a new method for obtaining the existence of exact solutionsand error estimations, based on the fixed point alternative (see also [?, ?]).Let (X, d) be a generalized metric space. An operator T : X → X satisfies a Lipschitz conditionwith the Lipschitz constant L if there exists a constant L ≥ ? such that d(Tx,Ty) ≤Ld(x, y) for all x, y ∈ X. If the Lipschitz constant L is less than ?, then the operator T iscalled a strictly contractive operator. Note that the distinction between the generalizedmetric and the usual metric is that the range of the former is permitted to include theinfinity. We recall the following theorem by Margolis and Diaz.
URI
http://link.springer.com/article/10.1186/1687-1847-2013-209http://hdl.handle.net/20.500.11754/44260
ISSN
1687-1847
DOI
10.1186/1687-1847-2013-209
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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