Abstract
We present an algorithm for extracting samples of homogeneity from functions between sets endowed with actions. In this way, we extend Taylor’s formula with the remainder of Peano type in a very wide framework. We illustrate the versatility of this procedure by giving approximations with polynomials of homogeneous functions for some non-differentiable functions.
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Dăianu, D.M.: Taylor type formula with Fréchet polynomials. Aequat. Math. 92, 695–707 (2018). https://doi.org/10.1007/s00010-018-0574-3
Dăianu, D.M., Mîndruţă, C.: Arithmetically homogeneous functions: characterizations, stability and hyperstability. Aequat. Math. 92, 1061–1077 (2018). https://doi.org/10.1007/s00010-018-0579-y
Podewski, K.P.: Topologisierung algebraischer Strukturen. Rev. Roumaine Math. Pures Appl. 22(9), 1283–1290 (1977)
Van der Lijn, G.: Les polynômes abstraits. Bull. Sci. Math. 84, 55–80, 102–112, 183–198 (1940)
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Dăianu, D.M. Samples of Homogeneous Functions. Results Math 77, 78 (2022). https://doi.org/10.1007/s00025-022-01614-7
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DOI: https://doi.org/10.1007/s00025-022-01614-7