Approximation properties of solutions of a mean value type functional inequalities

Volume 10, Issue 8, pp 4507--4514 http://dx.doi.org/10.22436/jnsa.010.08.42

Publication Date: August 29, 2017 Submission Date: June 21, 2017

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Authors

Ginkyu Choi - Department of Electronic and Electrical Engineering, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea. Soon-Mo Jung - Mathematics Section, College of Science and Technology, Hongik University, 30016 Sejong, Republic of Korea. Yang-Hi Lee - Department of Mathematics Education, Gongju National University of Education, Gongju 32553, Republic of Korea.

Abstract

We will prove the generalized Hyers-Ulam stability theorems of a mean value type functional equation, namely \[f(x) - g(y) = (x-y) h(sx + sy),\] which arises from the mean value theorem. As an application of our results, we introduce a characterization of quadratic polynomials.

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Keywords

• Hyers-Ulam stability
• generalized Hyers-Ulam stability
• mean value type functional equation
• characterization of quadratic polynomials.

MSC

•  39B82
•  39B62
•  39B52
•  46J99

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