TY - JOUR
AU - 박춘길
DA - 2013/07
PY - 2013
UR - http://link.springer.com/article/10.1186/1687-1847-2013-209
UR - http://hdl.handle.net/20.500.11754/44260
AB - 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.
PB - SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND
KW - heptic functional equation
KW - Hyers-Ulam stability
KW - fixed point method
KW - QUADRATIC FUNCTIONAL-EQUATION
KW - STABILITY
KW - ALGEBRAS
TI - Fixed points and approximately heptic mappings in non-Archimedean normed spaces
DO - 10.1186/1687-1847-2013-209
T2 - ADVANCES IN DIFFERENCE EQUATIONS
ER -