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Báo cáo hoa học: " On the stability of a mixed type functional equation in generalized functions"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: On the stability of a mixed type functional equation in generalized functions | Advances in Difference Equations SpringerOpen0 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. On the stability of a mixed type functional equation in generalized functions Advances in Difference Equations 2012 2012 16 doi 10.1186 1687-1847-2012-16 Young-Su Lee masuri@sogang.ac.kr ISSN 1687-1847 Article type Research Submission date 18 November 2011 Acceptance date 16 February 2012 Publication date 16 February 2012 Article URL http www.advancesindifferenceequations.com content 2012 1 16 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 Advances in Difference Equations go to http www.advancesindifferenceequations.com authors instructions For information about other SpringerOpen publications go to http www.springeropen.com 2012 Lee 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. On the stability of a mixed type functional equation in generalized functions Young-Su Lee Department of Mathematics Sogang University Seoul 121-741 Republic of Korea Email address masuri@sogang.ac.kr Abstract We reformulate the following mixed type quadratic and additive functional equa tion with n-independent variables 2f n n f xi - xj n 1 f xi n -1 f -xi 1 i j n i 1 i 1 i j as the equation for the spaces of generalized functions. Using the fundamental solution of the heat equation we solve the general solution and prove the Hyers-Ulam stability of this equation in the spaces of tempered distributions and Fourier hyperfunctions. Keywords quadratic functional equation additive functional