<abstract xmlns="http://www.w3.org/1999/xhtml"><p>L. Losonczi [4] determined local solutions of the generalized Cauchy equation <italic>f</italic>(<italic>F</italic> (<italic>x, y</italic>)) = <italic>f</italic>(<italic>x</italic>) + <italic>f</italic>(<italic>y</italic>) on components of the definition of a given associative rational function <italic>F.</italic> The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.</p></abstract>

L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F (x, y)) = f(x) + f(y) on components of the definition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.

Cauchy type functional equations related to some associative rational functions

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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{"article-title":"Cauchy type functional equations related to some associative rational functions"}

L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F (x, y)) = f(x) + f(y) on components of the definition of a given associative...

Cauchy type functional equations related to some associative rational functions

Published Online: Dec 05, 2019

Page range: 145 - 156

Received: May 22, 2019

Accepted: Jul 09, 2019

DOI: https://doi.org/10.2478/aupcsm-2019-0011

Keywords
functional equation, rational function, associativity

© 2019 Katarzyna Domańska, published by Sciendo

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Cauchy type functional equations related to some associative rational functions

Published Online: Dec 05, 2019

Page range: 145 - 156

Received: May 22, 2019

Accepted: Jul 09, 2019

DOI: https://doi.org/10.2478/aupcsm-2019-0011

Keywordsfunctional equation, rational function, associativity

© 2019 Katarzyna Domańska, published by Sciendo

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Keywords
functional equation, rational function, associativity