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Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II

Author

Listed:
  • Soon-Mo Jung

    (Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea
    These authors contributed equally to this work.)

  • Ki-Suk Lee

    (Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
    These authors contributed equally to this work.)

  • Michael Th. Rassias

    (Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
    These authors contributed equally to this work.)

  • Sung-Mo Yang

    (Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
    These authors contributed equally to this work.)

Abstract

Let X be a commutative normed algebra with a unit element e (or a normed field of characteristic different from 2), where the associated norm is sub-multiplicative. We prove the generalized Hyers-Ulam stability of a mean value-type functional equation, f ( x ) − g ( y ) = ( x − y ) h ( s x + t y ) , where f , g , h : X → X are functions. The above mean value-type equation plays an important role in the mean value theorem and has an interesting property that characterizes the polynomials of degree at most one. We also prove the Hyers-Ulam stability of that functional equation under some additional conditions.

Suggested Citation

  • Soon-Mo Jung & Ki-Suk Lee & Michael Th. Rassias & Sung-Mo Yang, 2020. "Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II," Mathematics, MDPI, vol. 8(8), pages 1-8, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1299-:d:395167
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    References listed on IDEAS

    as
    1. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, September.
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