16 research outputs found

    Some Remarks Concerning the General Octic Functional Equation

    No full text
    In this article, we study the stability of various forms for the general octic functional equation ∑i=099Ci−19−ifx+iy=0. We first find a special way of representing a given mapping as the sum of eight mappings. And by using the above representation, we will investigate the hyperstability of the general octic functional equation. Furthermore, we will discuss the Hyers–Ulam–Rassias stability of the general octic functional equation

    On the stability of bessel differential equation

    No full text
    Using power series method, Kim and Jung (2007) investigated the Hyers-Ulam stability of the Bessel differential equation, x^2y′′(x)+xy′(x)+(x^2−α^2)y(x) = 0, of order non-integral number α > 0. Also Bicer and Tunc (2017) obtained new sufficient conditions guaranteeing the Hyers-Ulam stability of Bessel differential equation of order zero. In this paper, by classical integral method we will investigate the stability of Bessel differential equations of a more generalized order than previous papers. Also, we will consider a more generalized domain (0, a) for any positive real number a while Kim and Jung (2007) restricted the domain near zero.publishe

    The Stability of a General Sextic Functional Equation by Fixed Point Theory

    No full text
    In this paper, we will consider the generalized sextic functional equation ∑i=07 7Ci−17−ifx+iy=0. And by applying the fixed point theorem in the sense of Ca˘dariu and Radu, we will discuss the stability of the solutions for this functional equation

    An Operator Method for the Stability of Inhomogeneous Wave Equations

    No full text
    In this paper, we will apply the operator method to prove the generalized Hyers-Ulam stability of the wave equation, u t t ( x , t ) − c 2 ▵ u ( x , t ) = f ( x , t ) , for a class of real-valued functions with continuous second partial derivatives. Finally, we will discuss the stability more explicitly by giving examples

    Some Properties of Approximate Solutions of Linear Differential Equations

    No full text
    In this paper, we will consider the Hyers-Ulam stability for the second order inhomogeneous linear differential equation, u ″ ( x ) + α u ′ ( x ) + β u ( x ) = r ( x ) , with constant coefficients. More precisely, we study the properties of the approximate solutions of the above differential equation in the class of twice continuously differentiable functions with suitable conditions and compare them with the solutions of the homogeneous differential equation u ″ ( x ) + α u ′ ( x ) + β u ( x ) = 0 . Several mathematicians have studied the approximate solutions of such differential equation and they obtained good results. In this paper, we use the classical integral method, via the Wronskian, to establish the stability of the second order inhomogeneous linear differential equation with constant coefficients and we will compare our result with previous ones. Specially, for any desired point c ∈ R we can have a good approximate solution near c with very small error estimation

    Approximation Property of the Stationary Stokes Equations with the Periodic Boundary Condition

    No full text
    In this paper, we will consider the stationary Stokes equations with the periodic boundary condition and we will study approximation property of the solutions by using the properties of the Fourier series. Finally, we will discuss that our estimation for approximate solutions is optimal

    Asymptotic aspect of derivations in Banach algebras

    No full text
    Abstract We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra

    Approximate Derivations with the Radical Ranges of Noncommutative Banach Algebras

    Get PDF
    We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras

    On the Intuitionistic Fuzzy Stability of Ring Homomorphism and Ring Derivation

    Get PDF
    We take into account the stability of ring homomorphism and ring derivation in intuitionistic fuzzy Banach algebra associated with the Jensen functional equation. In addition, we deal with the superstability of functional equation f(xy)=xf(y)+f(x)y in an intuitionistic fuzzy normed algebra with unit

    L

    Get PDF
    We consider the stability of stationary solutions w for the exterior Navier-Stokes flows with a nonzero constant velocity u∞ at infinity. For u∞=0 with nonzero stationary solution w, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal stability in Lp spaces for 11 and obtain Lr-Lp stability as Kozono and Ogawa and Borchers and Miyakawa obtained for u∞=0
    corecore