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http://dx.doi.org/10.14403/jcms.2016.29.2.287

THE GENERAL SOLUTION AND APPROXIMATIONS OF A DECIC TYPE FUNCTIONAL EQUATION IN VARIOUS NORMED SPACES  

Arunkumar, Mohan (Department of Mathematics Government Arts College)
Bodaghi, Abasalt (Department of Mathematics Garmsar Branch Islamic Azad University)
Rassias, John Michael (Pedagogical Department E.E. Section of Mathematics and Informatics National and Capodistrian University of Athens)
Sathya, Elumalai (Department of Mathematics Government Arts College)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.2, 2016 , pp. 287-328 More about this Journal
Abstract
In the current work, we define and find the general solution of the decic functional equation g(x + 5y) - 10g(x + 4y) + 45g(x + 3y) - 120g(x + 2y) + 210g(x + y) - 252g(x) + 210g(x - y) - 120g(x - 2y) + 45g(x - 3y) - 10g(x - 4y) + g(x - 5y) = 10!g(y) where 10! = 3628800. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in Banach spaces, generalized 2-normed spaces and random normed spaces by using direct and fixed point methods.
Keywords
Banach space; decic functional equation; generalized Ulam-Hyers stability; generalized 2-normed space; random normed space;
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