• Title/Summary/Keyword: generalized Hyers-Ulam stability

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QUALITATIVE ANALYSIS OF A PROPORTIONAL CAPUTO FRACTIONAL PANTOGRAPH DIFFERENTIAL EQUATION WITH MIXED NONLOCAL CONDITIONS

  • Khaminsou, Bounmy;Thaiprayoon, Chatthai;Sudsutad, Weerawat;Jose, Sayooj Aby
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.197-223
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    • 2021
  • In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

ON THE GENERALIZED HYERS-ULAM STABILITY OF A CUBIC FUNCTIONAL EQUATION

  • Jun, Kil-Woung;Lee, Sang-Baek
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.2
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    • pp.189-196
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    • 2006
  • The generalized Hyers-Ulam stability problems of the cubic functional equation f(x + y + z) + f(x + y - z) + 2f(x - y) + 4f(y) = f(x - y + z) + f(x - y - z) +2f(x + y) + 2f(y + z) + 2f(y - z) shall be treated under the approximately odd condition and the behavior of the cubic mappings and the additive mappings shall be investigated. The generalized Hyers-Ulam stability problem for functional equations had been posed by Th.M. Rassias and J. Tabor [7] in 1992.

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GENERALIZED HYERS-ULAM-RASSIAS STABILITY FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION IN QUASI-β-NORMED SPACES

  • Moradlou, Fridoun;Rassias, Themistocles M.
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.2061-2070
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    • 2013
  • In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

LOCAL STABILITY OF CAUCHY FUNCTIONAL EQUATION

  • Park, Kyoo-Hong;Lee, Young-Whan;Ji, Kyoung-Sihn
    • Journal of applied mathematics & informatics
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    • v.8 no.2
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    • pp.581-590
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    • 2001
  • In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.