Báo cáo hóa học: "Research Article Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces"

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 Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 589143 18 pages doi 2009 589143 Research Article Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces Liviu Cadariu1 and Viorel Radu2 1 Department of Mathematics Politehnica University of Timisoara Piaịa Victoriei number 2 300006 Timisoara Romania 2 Department of Mathematics Faculty of Mathematics and Computer Science West University ofTimi oara Vasile Parvan 4 300223 Timisoara Romania Correspondence should be addressed to Liviu Cadariu Received 24 April 2009 Accepted 19 October 2009 Recommended by Tomas Dominguez Benavides We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces which is then used to obtain stability properties for different kinds of functional equations linear functional equations generalized equation of the square root spiral generalized gamma equations in random normed spaces. As direct and natural consequences of our results we obtain general stability properties for the corresponding functional equations in deterministic metric and normed spaces. Copyright 2009 L. Cadariu and V. Radu. 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 Hyers 1 1941 has given an affirmative answer to a question of Ulam by proving the stability of additive Cauchy equations in Banach spaces. Then Aoki Bourgin Rassias Forti and Gajda considered the stability problem with unbounded Cauchy differences. Their results include the following theorem. Theorem see Hyers 1 Aoki 2 and Gajda 3 . Suppose that E is a real normed space F is a real Banach space and f E F is a given function such that the following condition holds f x y - f x - f y F d xllE y E z x y e E V1 for some p e 0

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