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- W4206631770 abstract "Abstract Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ 2 → S of the following parametric functional equation <m:math xmlns:m=http://www.w3.org/1998/Math/MathML display=block> <m:mrow> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:mo>+</m:mo> <m:mi>α</m:mi> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:mo>+</m:mo> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> <m:mo>+</m:mo> <m:mi>β</m:mi> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>1</m:mn> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>y</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:math> fleft( {{x_1} + {x_2} + alpha {y_1}{y_2},{x_1}{y_2} + {x_2}{y_1} + beta {y_1}{y_2}} right) = fleft( {{x_1},{y_1}} right)fleft( {{x_2},{y_2}} right), for all ( x 1 , y 1 ), ( x 2 , y 2 ) ∈ ℝ 2 , that generalizes some functional equations arising from number theory and is connected with the characterizations of the determinant of matrices." @default.
- W4206631770 created "2022-01-26" @default.
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- W4206631770 date "2022-01-17" @default.
- W4206631770 modified "2023-09-27" @default.
- W4206631770 title "A Parametric Functional Equation Originating from Number Theory" @default.
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- W4206631770 doi "https://doi.org/10.2478/amsil-2022-0001" @default.
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