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

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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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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.

GENERALIZED HYERS-ULAM STABILITY OF ADDITIVE FUNCTIONAL EQUATIONS

  • Kim, Hark-Mahn;Son, Eun-Yonug
    • The Pure and Applied Mathematics
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    • v.16 no.3
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    • pp.297-306
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    • 2009
  • In this paper, we obtain the general solution and the generalized HyersUlam stability theorem for an additive functional equation $af(x+y)+2f({\frac{x}{2}}+y)+2f(x+{\frac{y}{2})=(a+3)[f(x)+f(y)]$for any fixed integer a.

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STABILITY OF GENERALIZED QUADRATIC MAPPINGS IN FUZZY NORMED SPACES

  • Son, Eunyoung;Jun, Kil-Woung;Kim, Hark-Mahn
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.3
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    • pp.411-424
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    • 2010
  • In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.