tailieunhanh - Báo cáo hóa học: " Research Article A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution"

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 A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 839639 18 pages doi 2010 839639 Research Article A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution M. M. Pourpasha 1 J. M. Rassias 2 R. Saadati 3 and S. M. Vaezpour3 1 Department of Mathematics Science and Research Branch Islamic Azad University IAU Tehran Iran 2 Section of Mathematics and Informatics Pedagogical Department National and Kapodistrian University of Athens 4 Agamemnonos St. Aghia Paraskevi Athens 15342 Greece 3 Department of Mathematics Amirkabir University of Technology Hafez Avenue P. O. Box 15914 Tehran Iran Correspondence should be addressed to R. Saadati rsaadati@ and S. M. Vaezpour vaezpour@ Received 10 May 2010 Revised 13 July 2010 Accepted 31 July 2010 Academic Editor S. Reich Copyright 2010 M. M. Pourpasha 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. We apply the fixed point method to investigate the Hyers-Ulam stability of the Pexider functional equation f x y g x afy h x k y for all x y e E where E is a normed space and ơ E E is an involution. 1. Introduction and Preliminary A basic question in the theory of functional equations is as follows. When is it true that a function which approximately satisfies a functional equation must be close to an exact solution of the equation The first stability problem concerning group homomorphisms was raised by Ulam 1 in 1940 and affirmatively answered by Hyers in 2 . Subsequently the result of Hyers was generalized by Aoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias has provided a lot of influence in the development of what we now call Hyers-Ulam-Rassias stability of functional equations.