On Bounded Solutions of a Problem of R. Schilling
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چکیده
It is proved that if 0 < q ≤ (1− 3 √ 2 + 3 √ 4)/3, then the zero function is the only solution f : IR → IR of (1) satisfying (2) and bounded in a neighbourhood of at least one point of the set (3). The paper concerns bounded solutions f : IR → IR of the functional equation f(qx) = 1 4q [f(x − 1) + f(x + 1) + 2f(x)] (1) such that f(x) = 0 for | x |> Q (2) where q is a fixed number from the open interval (0, 1) and
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2 00 8 On bounded solutions of a problem of R . Schilling
It is proved that if 0 < q ≤ (1− 3 √ 2 + 3 √ 4)/3, then the zero function is the only solution f : IR → IR of (1) satisfying (2) and bounded in a neighbourhood of at least one point of the set (3). The paper concerns bounded solutions f : IR → IR of the functional equation f(qx) = 1 4q [f(x − 1) + f(x + 1) + 2f(x)] (1) such that f(x) = 0 for | x |> Q (2) where q is a fixed number from the open ...
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تاریخ انتشار 2008