Vol. 117, No. 1, 1985

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A problem on continuous and periodic functions

Jun Shung Hwang

Vol. 117 (1985), No. 1, 143–147
Abstract

Let f(x) be continuous and of period one on the real line. If dj, j = 1,2,,n, are n numbers such that each dj d1 is rational, then there are two rational numbers r and rfor which

f(r) ≤ f(r + dj) and  f(r′) ≥ f(r′+ dj),  j = 1,2,...,n.

This problem was communicated to the author by K. L. Chung and P. Erdös.

Mathematical Subject Classification 2000
Primary: 26A15
Milestones
Received: 18 March 1983
Published: 1 March 1985
Authors
Jun Shung Hwang