A Fixed Point Approach to the Stability of a Logarithmic Functional Equation

Soon-Mo Jung () and Themistocles M. Rassias ()
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Soon-Mo Jung: Mathematics Section, College of Science and Technology, Hongik University
Themistocles M. Rassias: National Technical University of Athens, Zografou Campus

Chapter Chapter 9 in Nonlinear Analysis and Variational Problems, 2010, pp 99-109 from Springer

Abstract: Abstract We will apply the fixed point method for proving the Hyers–Ulam–Rassias stability of a logarithmic functional equation of the form $$f(\sqrt{xy}) = \frac{1}{2} f(x) + \frac{1}{2} f(y),$$ where f: (0,∞) → E is a given function and E is a real (or complex) vector space.

Keywords: Banach Space; Functional Equation; Additive Mapping; Cauchy Sequence; Logarithmic Function (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-1-4419-0158-3_9

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