The General Solution and Approximations of a Decic Type Functional Equation in Various Normed Spaces

Abstract

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)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.

Trevigintic and quattuorvigintic functional equations in matrix normed spaces

“…They also presented some applications in non-linear analysis, especially in fixed point theory. This terminology may also be applied to the cases of other functional equations [2,3,10,13,16,19,20,23]. Also, the generalized Hyers-Ulam stability of functional equations and inequalities in matrix normed space has been studied by number of authors [7,8,15,18,22].…”

“…where 23! = 25852016740000000000000, is said to be trevigintic functional equation if the function ζ (u) = au 23 is its solution and Murali et al, [17] found the general solution of the following equation 2) in matrix paranormed spaces. The above equation is called quattuordecic functional equation if the function f (u) = au 24 is its solution.In this paper, we determine the general solution of the functional equation (1.1) and we also prove the stability of the functional equations (1.1) and (1.2) in matrix normed space with the help of fixed point method.…”

Mixed Q$_5$S$_6$, S$_7$O$_8$, N$_9$D$_{10}$ functional equations

“…The stability problems of the following functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [3,21,29,30]).…”

Ulam-Hyers stability of Euler-Lagrange additive functional equation in intuitionistic fuzzy Banach spaces: Direct and fixed point methods

“…On the other hand, Cȃdariu and Radu noticed that a fixed point alternative method is very important for the solution of the Ulam problem. In other words, they employed this fixed point method to the investigation of the Cauchy functional equation [13] and for the quadratic functional equation [12] (for more applications of this method, see [7] and [10]). The generalized Hyers-Ulam stability of different functional equations in intuitionistic fuzzy normed spaces has been studied by a number of the authors (see [3-6, 9, 11, 25-27, 35]).…”