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Journal of Shanghai University（Natural Science Edition）

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A Gauss Type Functional Equation with Four Means

FAN Li-xia1,2,LI Shi-jie3,ZHAO Ling-zhi1   

  1. 1. School of Sciences, Shanghai University, Shanghai 200444, China;2. Department of Mathematics, Jiaxing University, Jiaxing 314001, China;3. Department of Teaching Research, Quzhou Education Committee, Quzhou 324002, China
  • Received:2006-05-30 Revised:1900-01-01 Online:2007-04-30 Published:2007-04-30
  • Contact: FAN Li-xia

Cited

1

Abstract: A Gauss type functional equation is related to means. Gauss initially discussed a functional equation in terms of arithmetic mean and geometric mean. Haruki and Rassias studied a Gauss type functional equation with arithmetic mean and harmo nic mean using the Gaussian principle. Toader presented a Gauss type functional equation with power mean. Liu Zheng discussed a functional equation in terms of geometric mean and harmonic mean. However, none of these are associated with all the four means. This paper discusses a Gauss type functional equation having four Φi(i=1,2,3,4) means, and generalize the results of arithmetic mean, geometric mean, harmonic mean, and power mean.

Key words: weighted, Φi mean, Gauss funtional equation

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