báo cáo hóa học: Fuzzy Hyers-Ulam stability of an additive functional equation

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báo cáo hóa học:"Fuzzy Hyers-Ulam stability of an additive functional equation"Journal of Inequalities andApplications This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Fuzzy Hyers-Ulam stability of an additive functional equation Journal of Inequalities and Applications 2011, 2011:140 doi:10.1186/1029-242X-2011-140 Hassan Azadi Kenary (azadi@mail.yu.ac.ir) Hamid Rezaei (rezaei@mail.yu.ac.ir) Anoshiravan Ghaffaripour (an_ghaffaripour@mail.yu.ac.ir) Saedeh Talebzadeh (stmath@yahoo.com) Choonkil Park (baak@hanyang.ac.kr) Jung Rye Lee (jrlee@daejin.ac.kr) ISSN 1029-242X Article type Research Submission date 10 October 2011 Acceptance date 19 December 2011 Publication date 19 December 2011 Article URL http://www.journalofinequalitiesandapplications.com/content/2011/1/ This peer-reviewed article was published immediately upon acceptance. It can be downloaded, printed and distributed freely for any purposes (see copyright notice below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information about other SpringerOpen publications go to http://www.springeropen.com © 2011 Azadi Kenary et al. ; licensee Springer.This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Fuzzy Hyers-Ulam stability of an additive functional equation Hassan Azadi Kenary1 , Hamid Rezaei1 , Anoshiravan Ghaffaripour1 , Saedeh Talebzadeh2 , Choonkil Park3 , Jung Rye Lee∗4 1 Department of Mathematics, College of Sciences, Yasouj University, 75914-353 Yasouj, Iran 2 Department of Mathematics, Firoozabad Branch, Islamic Azad University, Firoozabad, Iran 3 Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea ∗4 Department of Mathematics, Daejin University, Kyeonggi 487-711, Korea Corresponding author: jrlee@daejin.ac.kr ∗ Email addresses: HAK: azadi@mail.yu.ac.ir HR: rezaei@mail.yu.ac.ir AG: an-ghaffaripour@mail.yu.ac.ir ST: stmath@yahoo.com CP: baak@hanyang.ac.krAbstract. In this paper, using the fixed point and direct methods, we prove the Hyers-Ulam stabilityof the following additive functional equation x+y+z 2f = f (x) + f (y ) + f (z ) (0.1) 2in fuzzy normed spaces. Keywords: Hyers-Ulam stability; additive functional equation; fuzzy normed space. Mathematics Subject Classification (2010): 39B22; 39B52; 39B82; 46S10; 47S10;46S40. 1. Introduction A classical question in the theory of functional equations is the following: When isit true that a function which approximately satisfies a functional equation must be closeto an exact solution of the equation? If the problem accepts a solution, we say thatthe equation is stable. The first stability problem concerning group homomorphisms wasraised by Ulam [1] in 1940. In the next year, Hyers [2] gave a positive answer to the abovequestion for additive groups under the assumption that the groups are Banach spaces. In1978, Rassias [3] proved a generalization of the Hyers’ theorem for additive mappings.Theorem 1.1. (Th.M. Rassias) Let f : X → Y be a mapping from a normed vector spaceX into a Banach space Y subject to the inequality p ...