The Experts below are selected from a list of 14190 Experts worldwide ranked by ideXlab platform

John Michael Rassias - One of the best experts on this subject based on the ideXlab platform.

Jinrong Wang - One of the best experts on this subject based on the ideXlab platform.

Ioan A. Rus - One of the best experts on this subject based on the ideXlab platform.

  • Ulam Stability of the Operatorial Equations
    Functional Equations in Mathematical Analysis, 2011
    Co-Authors: Ioan A. Rus
    Abstract:

    Let (E, +, ℝ, ≤, → ) be an ordered linear L-space, \({E}_{+} :=\{ e \in E\ \vert \ e \geq 0\}\), (X, d) and (Y, ρ) be two generalized metric spaces with d(x, y), ρ(x, y) ∈ E +, and f, g : X → Y be two operators. In this paper we present for the coincidence equation $$f(x) = g(x)$$ four types of Ulam stability: Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability. Some illustrative examples are given, the relations of Ulam stability with the weakly Picard operator are studied and two research directions are also presented.

  • Ulam stabilities of ordinary differential equations in a Banach space
    2010
    Co-Authors: Ioan A. Rus
    Abstract:

    Let (B;j j ) be a Banach space, A : B ! B be the infinitesimal generator of a C0- semigroup, I := (a;b) or (a;+1( and f 2 C(I B;B). In this paper we present and discuss four types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the following differential equation u 0 (t) = A(u(t)) +f(t;u(t)); t2 I:

  • REMARKS ON Ulam STABILITY OF THE OPERATORIAL EQUATIONS
    2009
    Co-Authors: Ioan A. Rus
    Abstract:

    In this paper we present four types of Ulam stability for operatorial equations: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability. The relations of Ulam stability with the c-weakly Picard operators are also studied. Some examples and counterexamples are given.

  • Ulam stability of ordinary differential equations
    2009
    Co-Authors: Ioan A. Rus
    Abstract:

    In this paper we present four types of Ulam stability for ordinary dierential equations: Ulam-Hyers stability, generalized Ulam- Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers- Rassias stability. Some examples and counterexamples are given.

Aghia Paraskevi - One of the best experts on this subject based on the ideXlab platform.

  • Ulam STABILITY OF RECIPROCAL DIFFERENCE AND ADJOINT FUNCTIONAL EQUATIONS
    2011
    Co-Authors: K. Ravi, John Michael Rassias, B. V. Senthil Kumar, Aghia Paraskevi
    Abstract:

    In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or Ulam-Gavruta-Rassias) stability problem for the same equations.

  • ON THE Ulam STABILITY FOR EULER-LAGRANGE TYPE QUADRATIC FUNCTIONAL EQUATIONS
    2005
    Co-Authors: Matina John Rassias, John Michael Rassias, Aghia Paraskevi
    Abstract:

    In 1940 (and 1968) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D.H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1951 D. G. Bourgin has been the second author treating the Ulam problem for additive mappings. In 1978 according to P.M. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-2004 we established the Hyers-Ulam stability for the Ulam problem for different mappings. In 1992-2000 J.M. Rassias investigated the Ulam stability for Euler-Lagrange mappings. In this article we solve the Ulam problem for Euler-Lagrange type quadratic functional equations. These stability results can be applied in mathematical statistics, stochastic analysis, algebra, geometry, as well as in psychology and sociology.

  • The Ulam stability problem in approximation of approximately quadratic mappings by quadratic mappings.
    Journal of Inequalities in Pure & Applied Mathematics, 2004
    Co-Authors: John Michael Rassias, Aghia Paraskevi
    Abstract:

    S.M. Ulam, 1940, proposed the well-known Ulam stability problem and in 1941, the problem for linear mappings was solved by D.H. Hyers. D.G. Bourgin, 1951, also investigated the Ulam problem for additive mappings. P.M. Gruber, claimed, in 1978, that this kind of stability problem is of particular interest in probability theory and in the case of functional equations of different types. F. Skof, in 1981, was the first author to solve the Ulam problem for quadratic mappings. During the years 1982-1998, the author established the Hyers-Ulam stability for the Ulam problem for different mappings. In this paper we solve the Ulam stability problem by establishing an approximation of approximately quadratic mappings by quadratic mappings. Today there are applications in actuarial and financial mathematics, sociology and psychology, as well as in algebra and geometry.

K. Shah - One of the best experts on this subject based on the ideXlab platform.

  • Ulam–Hyers Stability Analysis of a Three-Point Boundary-Value Problem for Fractional Differential Equations
    Ukrainian Mathematical Journal, 2020
    Co-Authors: A. Ali, K. Shah
    Abstract:

    We study the problem of existence and uniqueness of the solution of a three-point boundary-value problem for a differential equation of fractional order. Further, we investigate various kinds of the Ulam stability, such as the Ulam–Hyers stability, the generalized Ulam–Hyers stability, the Ulam–Hyers–Rassias stability, and the generalized Ulam–Hyers–Rassias stability for the analyzed problem. We also present examples to explain our results.

  • on Ulam s stability for a coupled systems of nonlinear implicit fractional differential equations
    Bulletin of the Malaysian Mathematical Sciences Society, 2019
    Co-Authors: Zeeshan Ali, Akbar Zada, K. Shah
    Abstract:

    In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractional differential equations involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach contraction principle and Leray–Schauder of cone type. For stability, we utilize classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

  • Ulam stability results for the solutions of nonlinear implicit fractional order differential equations
    Hacettepe Journal of Mathematics and Statistics, 2018
    Co-Authors: Zeeshan Ali, Akbar Zada, K. Shah
    Abstract:

    In this manuscript, we study the existence and uniqueness of solution for a class of fractional order boundary value problem (FBVP) for implicit fractional differential equations with Riemann-Liouville derivative. Furthermore, we investigate different kinds of Ulam stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the proposed problem. The concerned analysis is carried out through using classical technique of nonlinear functional analysis. The main results are illustrated by providing a couple of examples