Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2016.01.08
  • Accepted : 2016.05.09
  • Published : 2016.05.15
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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.

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