tailieunhanh - Báo cáo hóa học: " Review Article Nonlinear L-Random Stability of an ACQ Functional Equation"

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: Review Article Nonlinear L-Random Stability of an ACQ Functional Equation | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 194394 23 pages doi 2011 194394 Review Article Nonlinear L-Random Stability of an ACQ Functional Equation Reza Saadati M. M. Zohdi and S. M. Vaezpour Department of Mathematics Science and Research Branch Islamic Azad University Ashrafi Esfahani Ave Tehran 14778 Iran Correspondence should be addressed to Reza Saadati rsaadati@ Received 9 December 2010 Accepted 6 February 2011 Academic Editor Soo Hak Sung Copyright 2011 Reza Saadati 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 prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation 11 x 2y 11 x - 2y 44f x y 44 f x - y 12 f 3y - 48f 2y 60 f y - 66 f x in complete latticetic random normed spaces. 1. Introduction Random theory is a powerful hand set for modeling uncertainty and vagueness in various problems arising in the field of science and engineering. It has also very useful applications in various fields for example population dynamics chaos control computer programming nonlinear dynamical systems nonlinear operators statistical convergence and so forth. The random topology proves to be a very useful tool to deal with such situations where the use of classical theories breaks down. The usual uncertainty principle of Werner Heisenberg leads to a generalized uncertainty principle which has been motivated by string theory and noncommutative geometry. In strong quantum gravity regime space-time points are determined in a random manner. Thus impossibility of determining the position of particles gives the space-time a random structure. Because of this random structure position space representation of quantum mechanics breaks down and therefore a generalized normed space of quasiposition .