TAILIEUCHUNG - Báo cáo sinh học: " Research Article Stabilities of Cubic Mappings in Fuzzy Normed Spaces"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Stabilities of Cubic Mappings in Fuzzy Normed Spaces | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID i5o873 15 pages doi 2010 150873 Research Article Stabilities of Cubic Mappings in Fuzzy Normed Spaces Ali Ghaffari and Ahmad Alinejad Department of Mathematics Semnan University . Box 35195-363 Semnan Iran Correspondence should be addressed to Ali Ghaffari aghaffari@ Received 15 January 2010 Revised 19 April 2010 Accepted 11 May 2010 Academic Editor T. Bhaskar Copyright 2010 A. Ghaffari and A. Alinejad. 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. Rassias 2001 introduced the pioneering cubic functional equation in the history of mathematical analysis f x 2y - 3f x y 3f x - f x - y 6f y and solved the pertinent famous Ulam stability problem for this inspiring equation. This Rassias cubic functional equation was the historic transition from the following famous Euler-Lagrange-Rassias quadratic functional equation f x y -2f x f x-y 2f y to the cubic functional equations. In this paper we prove the Ulam-Hyers stability of the cubic functional equation f x 3y -3f x y 3f y-x -f x-3y 48f y in fuzzy normed linear spaces. We use the definition of fuzzy normed linear spaces to establish a fuzzy version of a generalized Hyers-Ulam-Rassias stability for above equation in the fuzzy normed linear space setting. The fuzzy sequentially continuity of the cubic mappings is discussed. 1. Introduction Studies on fuzzy normed linear spaces are relatively recent in the field of fuzzy functional analysis. The notion of fuzzyness has a wide application in many areas of science. In 1984 Katsaras 1 first introduced a definition of fuzzy norm on a linear space. Later several notions of fuzzy norm have been introduced and discussed from different points of view 2 3 . Concepts of sectional fuzzy continuous mappings and .

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