منابع مشابه
Orthogonal stability of mixed type additive and cubic functional equations
In this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$ is orthogonality in the sense of Ratz.
متن کاملAnalytic Solutions for Iterative Functional Differential Equations
Because of its technical difficulties the existence of analytic solutions to the iterative differential equation x′(z) = x(az + bx(z) + cx′(z)) is a source of open problems. In this article we obtain analytic solutions, using Schauder’s fixed point theorem. Also we present a unique solution which is a nonconstant polynomial in the complex field.
متن کاملSmooth Solutions of a Class of Iterative Functional Differential Equations
and Applied Analysis 3 where i, j, and k are nonnegative integers. Let I be a closed interval in R. By induction, we may prove that x∗jk t Pjk ( x10 t , . . . , x1,j−1 t ; . . . ;xk0 t , . . . , xk,j−1 t ) , 1.11 βjk Pjk ⎛ ⎜⎝ j terms { }} { x′ ξ , . . . , x′ ξ ; . . . ; j terms { }} { x k ξ , . . . , x k ξ ⎞ ⎟⎠, 1.12 Hjk Pjk ⎛ ⎜⎝ j terms { }} { 1, . . . , 1; j terms { }} { M2, . . . ,M2; . . . ...
متن کاملOn Cauchy-type functional equations
LetG be a Hausdorff topological locally compact group. LetM(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n ≥ 1 and all μ ∈ M(G), we consider the functional equations ∫ G f(xty)dμ(t) = ∑n i=1gi(x)hi(y), x,y ∈ G, where the functions f , {gi}, {hi}: G → C to be determined are bounded and continuous functions on G. We show how the solutions of these equati...
متن کاملIterative Approximation of Solutions of Nonlinear Equations of Hammerstein Type
Suppose X is a real q-uniformly smooth Banach space and F,K : X → X with D(K) = F(X) = X are accretive maps. Under various continuity assumptions on F and K such that 0 = u+KFu has a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X . Our method...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1997
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700030872