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Functional Equations — Results and Advances pp 81–87Cite as

On a Mikusiński—Jensen Functional Equation

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Part of the book series: Advances in Mathematics ((ADMA,volume 3))

Abstract

The following Mikusinski-Jensen type functional equation

EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaWaaSaaaeaacaWG4bGaey4kaSIaamyEaaqaaiaaikdaaaaacaGL % OaGaayzkaaWaamWaaeaacaWGMbWaaeWaaeaacaWG4baacaGLOaGaay % zkaaGaey4kaSIaamOzamaabmaabaGaamyEaaGaayjkaiaawMcaaiab % gkHiTiaaikdacaWGMbWaaeWaaeaadaWcaaqaaiaadIhacqGHRaWkca % WG5baabaGaaGOmaaaaaiaawIcacaGLPaaaaiaawUfacaGLDbaacqGH % 9aqpcaaIWaGaaGzaVpaabmaabaGaamiEaiaacYcacaWG5bGaeyicI4 % SaamysaaGaayjkaiaawMcaaaaa!575E!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$f\left( {\frac{{x + y}}{2}} \right)\left[ {f\left( x \right) + f\left( y \right) - 2f\left( {\frac{{x + y}}{2}} \right)} \right] = 0\left( {x,y \in I} \right)$$

is investigated. The main result states that if I is an open real interval, or more generally, if I is a convex subset of a linear space whose intersection with straight lines is an open segment, then the above equation is equivalent to the so called Jensen functional equation.

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References

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, University of Debrecen, H-4010, Debrecen, Pf. 12, Hungary

    Károly Lajkó & Zsolt Páles

Authors
  1. Károly Lajkó
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  2. Zsolt Páles
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Editors and Affiliations

  1. Institute of Mathematics and Informatics, University of Debrecen, Hungary

    Zoltán Daróczy  & Zsolt Páles  & 

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Dedicated to the 70th birthday of Professor Mátyás Arató

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© 2002 Springer Science+Business Media Dordrecht

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Lajkó, K., Páles, Z. (2002). On a Mikusiński—Jensen Functional Equation. In: Daróczy, Z., Páles, Z. (eds) Functional Equations — Results and Advances. Advances in Mathematics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5288-5_6

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  • DOI: https://doi.org/10.1007/978-1-4757-5288-5_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5210-3

  • Online ISBN: 978-1-4757-5288-5

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