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Survey on Cauchy Functional Equation in Lattice Environments

  • Nutefe Kwami AgbekoEmail author
Chapter

Abstract

By replacing in Cauchy functional equation the addition with the lattice operations we are able to formulate the Ulam’s stability problem in lattice environments. Various types of solution are formulated and proved similarly as their counterparts in addition environments. This survey contains a part of the habilitation thesis presented to the Department of Mathematics, University of Debrecen (cf. Agbeko, Studies on some addition-free environments. Habilitation Thesis submitted to the University of Debrecen. http://www.uni-miskolc.hu/~matagbek/Habilitation%20Thesis.pdf) and the material in Agbeko and Szokol (Extracta Math 33:1–10, 2018).

Keywords

Functional equation Functional inequality Banach lattice Ulam’s stability Lattice semigroup 

Mathematics Subject Classification (2010)

Primary 39B82 06B99 20M99; Secondary 39B42 39B52 46A40 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of MiskolcMiskolcHungary

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