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Article

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

by 1,*,†, 2,†, 3,† and 2,†
1
Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Korea
2
Department of Mathematics Education, Korea National University of Education, Cheongju 28173, Korea
3
Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(8), 1299; https://doi.org/10.3390/math8081299
Received: 22 July 2020 / Revised: 29 July 2020 / Accepted: 5 August 2020 / Published: 6 August 2020
(This article belongs to the Special Issue New Trends in Functional Equation)
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)=(xy)h(sx+ty), where f,g,h:XX 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. View Full-Text
Keywords: Hyers-Ulam stability; Hyers-Ulam-Rassias stability; generalized Hyers-Ulam stability; mean value-type functional equation Hyers-Ulam stability; Hyers-Ulam-Rassias stability; generalized Hyers-Ulam stability; mean value-type functional equation
MDPI and ACS Style

Jung, S.-M.; Lee, K.-S.; Rassias, M.T.; Yang, S.-M. Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II. Mathematics 2020, 8, 1299. https://doi.org/10.3390/math8081299

AMA Style

Jung S-M, Lee K-S, Rassias MT, Yang S-M. Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II. Mathematics. 2020; 8(8):1299. https://doi.org/10.3390/math8081299

Chicago/Turabian Style

Jung, Soon-Mo, Ki-Suk Lee, Michael T. Rassias, and Sung-Mo Yang. 2020. "Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II" Mathematics 8, no. 8: 1299. https://doi.org/10.3390/math8081299

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