Approximation Properties of Solutions of a Mean Value-Type Functional Inequality, II
Soon-Mo Jung, Ki-Suk Lee, Michael Th. Rassias, Sungmo Yang
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(sx+ty), 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.
Topics & Concepts
MathematicsFunctional equationMultiplicative functionNorm (philosophy)Type (biology)Commutative propertyPure mathematicsStability (learning theory)Unit (ring theory)Discrete mathematicsMathematical analysisDifferential equationBiologyMathematics educationPolitical scienceComputer scienceMachine learningEcologyLawFunctional Equations Stability Results