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Báo cáo hóa học: " Research Article A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences"

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 Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 793947 10 pages doi 10.1155 2010 793947 Research Article A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences Janusz Brzdek1 and Soon-Mo Jung2 1 Department of Mathematics Pedagogical University Podchorazych 2 30-084 Krakow Poland 2 Mathematics Section College of Science and Technology Hongik University 339-701 Jochiwon Republic of Korea Correspondence should be addressed to Soon-Mo Jung smjung@hongik.ac.kr Received 26 April 2010 Accepted 15 July 2010 Academic Editor Ram N. Mohapatra Copyright 2010 J. Brzdek and S.-M. Jung. 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 prove the Hyers-Ulam stability of a second-order linear functional equation in single variable with constant coefficients that is connected with the Fibonacci numbers and Lucas sequences. In this way we complement extend and or improve some recently published results on stability of that equation. 1. Introduction In this paper C R Z and N stand as usual for the sets of complex numbers real numbers integers and positive integers respectively. Let S be a nonempty set ị S S X be a Banach space over a field K e C R p q e K q f- 0 and a1 a2 denote the complex roots of the equation x2 - px q 0. 1.1 Moreover ị0 x x ịn 1 x ị ịn x and only for bijective ị ị-n-1 x ị-1 ị-n x for x e S and n e N0 N u 0 . The problem of stability of functional equations was motivated by a question of Ulam asked in 1940 and a solution to it by Hyers published in 1 . Since then numerous papers have been published on that subject and we refer to 2-7 for more details some discussions 2 Journal of Inequalities and Applications and further references for examples of very recent results see for example 8-12 .