共查询到20条相似文献,搜索用时 31 毫秒
1.
P. K. SAHO 《数学学报(英文版)》2005,21(5):1159-1166
In this paper, we determine the general solution of the functional equation f1 (2x + y) + f2(2x - y) = f3(x + y) + f4(x - y) + f5(x) without assuming any regularity condition on the unknown functions f1,f2,f3, f4, f5 : R→R. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x - y) = g(x + y) + g(x - y) + h(x) and f(2x + y) - f(2x - y) = g(x + y) - g(x - y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszfi. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. 相似文献
2.
A. Firat 《Siberian Mathematical Journal》2006,47(1):169-172
Given a prime ring R, a skew g-derivation for g : R → R is an additive map f : R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x)) = g(f(x)) for all x, y ∈ R. We generalize some properties of prime rings with derivations to the class of prime rings with skew derivations. 相似文献
3.
JAEYOUNG CHUNG HEATHER HUNT ALLISON PERKINS PRASANNA K SAHOO 《Proceedings Mathematical Sciences》2014,124(3):365-381
In this paper, we study the Hyers–Ulam stability of a simple Levi–Civitá functional equation f(x+y)=f(x)h(y)+f(y) and its pexiderization f(x+y)= g(x) h(y)+k(y) on non-unital commutative semigroups by investigating the functional inequalities |f(x+y)?f(x)h(y)?f(y)|≤?? and |f(x+y)?g(x)h(y)?k(y)|≤??, respectively. We also study the bounded solutions of the simple Levi–Civitá functional inequality. 相似文献
4.
In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability
of the functional equation
6f(x + y) - 6f(x - y) + 4f(3y) = 3f(x + 2y) - 3f(x - 2y) + 9f(2y)6f(x + y) - 6f(x - y) + 4f(3y) = 3f(x + 2y) - 3f(x - 2y) + 9f(2y) 相似文献
5.
J. Dombi 《Fuzzy Sets and Systems》1982,8(2):149-163
In this paper we examine operators which can be derived from the general solution of functional equations on associativity. We define the characteristics of those functions f(x) which are necessary for the production of operators. We shall show, that with the help of the negation operator for every such function f(x) a function g(x) can be given, from which a disjunctive operator can be derived, and for the three operators the DeMorgan identity is fulfilled. For the fulfillment of the DeMorgan identity the necessary and sufficient conditions are given.We shall also show that an fλ(x) can be constructed for every f(x), so that for the derived kλ(x,y) and dλ(x,y) limλ→∞kλ(x,y) and limλ→∞dλ(x,y) = max(x,y).As Yager's operator is not reducible, for every λ there exists an α, for which, in case x < α and y<α, kλ(x,y) = 0.We shall give an f(x) which has the characteristics of Yager's operator, and which is strictly monotone.Finally we shall show, that with the help of all those f(x), which are necessary when constructing a k(x,y), an F(x) can be constructed which has the properties of the measures of fuzziness introduced by A. De Luca and S. Termini. Some classical fuzziness measures are obtained as special cases of our system. 相似文献
6.
Soon-Mo Jung 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2000,70(1):175-190
We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik,
and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic
functional equation of Pexider type,f
1 (x +y) + f2(x -y) =f
3(x) +f
4(y), for a large class of functions. 相似文献
7.
A. M. D’yachenko 《Moscow University Mathematics Bulletin》2010,65(2):55-62
The pointwise behavior of partial sums and Cesàro means of trigonometric series were studied in many papers. This paper deals with the behavior of rectangular Cesàro means at a point (x 0, y 0) for functions f(x, y) bounded in the square [?π; π]2 and satisfying the condition |f(x 0 + s, y 0 + t) ? f(x 0, y 0)| ≤ ρ $ \left( {\sqrt {s^2 + t^2 } } \right) $ α , for some α ∈ (0, 1) and all s and t. 相似文献
8.
In this paper we establish the general solution of the functional equation 6f(x+y)−6f(x−y)+4f(3y)=3f(x+2y)−3f(x−2y)+9f(2y) and investigate the Hyers-Ulam-Rassias stability of this equation. 相似文献
9.
10.
《Journal of Computational and Applied Mathematics》1988,24(3):393-397
For the numerical integration of general second-order initial-value problems y″ = f(x, y, y′), y(x0) = y0, y′(x0) = y′0, we report a family of two-step sixth-order methods which are superstable for the test equation y″ + 2αy′ + β2y = 0, α, β ⩾ 0, α + β\s>0, in the sense of Chawla [1]. 相似文献
11.
Oscar Rojo 《Journal of Mathematical Analysis and Applications》1977,61(1):208-215
This paper considers a problem proposed by Bellman in 1970: given a continuous kernel K(x, y) defined on I × I, find a pair of continuous functions f and g such that f(x) + g(y) ? K(x, y) on I × I and ∝I (f + g) is minimum. The notion of basic decomposition of K is defined, and it is shown that whenever K(x, y) or K(x, a + b ? y), I = [a, b], admits a basic decomposition, Bellman's problem has a unique differentiable solution, provided K is differentiable. Explicit formulas for such solutions are given. More generally, there are kernels which admit basic decompositions on subintervals which can be “pasted together” to define a unique piecewise differentiable solution. 相似文献
12.
This paper deals with the nonlinear two point boundary value problem y″ = f(x, y, y′, R1,…, Rn), x0 < x < xfS1y(x0) + S2y′(x0) = S3, S4y(xf) + S5y′(xf) = S6 where R1,…, Rn, S1,…, S6 are bounded continuous random variables. An approximate probability distribution function for y(x) is constructed by numerical integration of a set of related deterministic problems. Two distinct methods are described, and in each case convergence of the approximate distribution function to the actual distribution function is established. Primary attention is placed on problems with two random variables, but various generalizations are noted. As an example, a nonlinear one-dimensional heat conduction problem containing one or two random variables is studied in some detail. 相似文献
13.
In the previous researches [2,3] b-integer and b-decimal parts of real numbers were introduced and studied by M.H. Hooshmand. The b-parts real functions have many interesting number theoretic explanations, analytic and algebraic properties, and satisfy the functional equation f (f(x) + y - f(y)) = f(x). These functions have led him to a more general topic in semigroups and groups (even in an arbitrary set with a binary operation [4] and the following functional equations have been introduced: Associative equations: f(xf(yz))=f(f(xy)z),f(xf(yz))=f(f(xy)z)=f(xyz) | . Decomposer equations:
f(f(x)-f(y)) £ f(x+y) + f(f(x-y)) -f(x) - f(y), f(f(x)-f(y)) £ f(f(x+y)) + f(x-y) -f(x) - f(y), f(f(x)-f(y)) £ f(f(x+y)) + f(f(x-y)) -f(f(x)) - f(y),\begin{gathered}f(f(x)-f(y)) \leq f(x+y) + f(f(x-y)) -f(x) - f(y), \hfill \\ f(f(x)-f(y)) \leq f(f(x+y)) + f(x-y) -f(x) - f(y), \hfill \\ f(f(x)-f(y)) \leq f(f(x+y)) + f(f(x-y)) -f(f(x)) - f(y),\end{gathered} 相似文献
18.
《Journal of Computational and Applied Mathematics》1999,102(2):315-331
In this paper, on the basis of the results of Ishihara et al. (1997), we first discuss global convergence theorems for the improved SOR-Newton and block SOR-Newton methods with orderings applied to a system of mildly nonlinear equations, which includes as a special case the discretized version of the Dirichlet problem, for the equation ϵΔu + p(x)ux + q(y)uy = f(x, y, u), where f is continuously differentiable and fu(x, y, u) ⩾ 0. Moreover, we propose a practical choice of the multiple relaxation parameters {ωi} for them. Numerical examples are also given. 相似文献
19.
Abbas Najati 《Journal of Mathematical Analysis and Applications》2008,340(1):569-574
In this paper, we prove the generalized Hyers-Ulam stability for the following quartic functional equation
f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y). 相似文献
20.
In this paper, we solve a new functional equation
f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) 相似文献
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