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Summary. We rephrase Lemma 2.3 from (M. Sablik, Taylor’s theorem and functional equations, Aequationes Math. 60 (2000), 258–267) in order to solve two functional equations. First, the following “Taylor-like” functional equation $$ f(x)\, = \,{\sum\limits_{k = 0}^n {g_{k} (x + t(y - x))((t(x - y))^{k} ) + (\Phi (x) - \Phi (y))((t(x - y))^{n} )} } $$ and a second one stemming from Simpson’s rule:...
Summary. We introduce a method of solving a wide range of functional equations stemming from Mean Value Theorems. We generalize the results of Z. Daróczy and Gy. Maksa (Corollary 2; [2]) in the spirit of M. Sablik’s lemma (Lemma 2.3; [11]). Next, we illustrate the method taking into account two functional equations. The first one is connected with Flett’s Mean Value Theorem ([6]) and the second one...
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