tailieunhanh - báo cáo hóa học:" Research Article Generalized Ulam-Hyers Stability of ˇ Jensen Functional Equation in Serstnev PN 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 Generalized Ulam-Hyers Stability of ˇ Jensen Functional Equation in Serstnev PN Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 868193 14 pages doi 2010 868193 Research Article Generalized Ulam-Hyers Stability of Jensen Functional Equation in Serstnev PN Spaces M. Eshaghi Gordji 1 M. B. Ghaemi 2 H. Majani 2 and C. Park3 1 Department of Mathematics Semnan University . Box 35195-363 Semnan Iran 2 Department of Mathematics Iran University of Science and Technology Narmak Tehran Iran 3 Department of Mathematics Hanyang University Seoul 133-791 South Korea Correspondence should be addressed to C. Park baak@ Received 17 November 2009 Revised 31 January 2010 Accepted 1 March 2010 Academic Editor Sin-Ei Takahasi Copyright 2010 M. Eshaghi Gordji 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 establish a generalized Ulam-Hyers stability theorem in a Serstnev probabilistic normed space briefly Serstnev PN-space endowed with Hm- In particular we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a Serstnev PN-space is continuous at a point then we can approximate it by an everywhere continuous Jensen mapping. As a version of a theorem of Schwaiger we also show that if every approximate Jensen type mapping from the natural numbers into a Serstnev PN-space can be approximated by an additive mapping then the norm of Serstnev PN-space is complete. 1. Introduction and Preliminaries Menger proposed transferring the probabilistic notions of quantum mechanic from physics to the underlying geometry. The theory of probabilistic normed spaces briefly PN-spaces is important as a generalization of deterministic result of linear normed spaces and also in the study of random operator equations. The notion of a probabilistic normed space was introduced by Serstnev 1 .