Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
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: Research Article On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 902187 11 pages doi 10.1155 2008 902187 Research Article On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces E. Baktash 1 Y. J. Cho 2 M. Jalili 3 R. Saadati 4 5 and S. M. Vaezpour4 1 Youngs Researchers Club and Department of Basic Sciences Islamic Azad University Ayatollah Amoli Branch P.O. Box 678 Amol Iran 2 Department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 South Korea 3 Department of Mechanical Engineering Islamic Azad University Ayatollah Amoli Branch P.O. Box 678 Amol Iran 4 Department of Mathematics and Computer Science Amirkabir University of Technology 424 Hafez Avenue Tehran 15914 Iran 5 Faculty of Sciences University ofShomal P.O. Box 731 Amol Iran Correspondence should be addressed to Y. J. Cho yjcho@gsnu.ac.kr Received 27 August 2008 Revised 23 October 2008 Accepted 24 November 2008 Recommended by Wing-Sum Cheung Recently the stability of the cubic functional equation f 2x y f 2x - y 2f x y 2f x -y 12f x in fuzzy normed spaces was proved in earlier work and the stability of the additive functional equations f x y f x f y 2f x y 2 f x f y in random normed spaces was proved as well. In this paper we prove the stability of the cubic functional equation f 2x y f 2x - y 2f x y 2f x - y 12f x in random normed spaces by an alternative proof which provides a better estimation. Finally we prove the stability of the quartic functional equation f 2x y f 2x - y 4f x y 4f x - y 24f x - 6f y in random normed spaces. Copyright 2008 E. Baktash et al. 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. 1. Introduction and preliminaries The study of stability problems for functional equations is related to a question of Ulam 1 concerning the .
