Inequalities and Identities Involving Sums of Integer Functions
نویسنده
چکیده
The floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively. More precisely, the floor function ⌊x⌋ is the largest integer not greater than x and the ceiling function ⌈x⌉ is the smallest integer not less than x. Iverson [7, p. 127] introduced this notation and the terms floor and ceiling in the early 1960’s and now this notation is standard in most areas of mathematics. Many properties of floor and ceiling functions are presented in [1, 5]. If x, y are real numbers and n is an integer so that y − x < 1 and x ≤ n ≤ y then
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تاریخ انتشار 2011