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Geometric meaning of Cauchy functional equation

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#real-analysis #geometry #functional-equations
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Solve the functional equation $f(xf(y)+x)=xy+f(x)$

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#functional-equations
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Criteria for elevating a rational FE solution to reals

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#functional-equations
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Solutions of the functional equation $f(x) + f(qx) = 0$

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#calculus #real-analysis #functional-equations
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Solutions of the functional equation $f(2x) = \frac{f(x)+x}{2}$

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#calculus #real-analysis #functions #functional-equations
328
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Is the product rule for logarithms an if-and-only-if statement?

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#logarithms #functional-equations
388
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Find $f''(x)$ if $f\circ f'(x) = 4x^2 + 3$

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#derivatives #functional-equations #function-and-relation-composition
351
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Commutative version of hyperoperators

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#commutative-algebra #functional-equations #hyperoperation
122
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Functional equation $f(x+1)-f(x)=nf(x)$

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#functional-equations
2.4k
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Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?

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#functions #trigonometry #functional-equations
397
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Solve the following functional equation: $[f(x)+f(y)][f(x+2y)+f(y)]=[f(x+y)]^2+f(2y)f(y)$

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#functional-equations
229
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Functional equation $f(x+y)f(x-y)=\big(f(x)+f(y)\big)^2-4x^2f(y)$, extended solution

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#functional-equations
154
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Role of functional equations in current panorama of pure mathematics

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#analysis #reference-request #soft-question #functional-equations #big-picture
417
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Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$

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#polynomials #functional-equations
250
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Solutions to functional equation $ \gamma(s,t)=f(t \cdot g(s))+h(t) $

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#functional-equations

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