Applied Mathematics E-Notes, 26(2026), 254-262.

Majorization Involving The Cyclic Moving Average And Its Applications

Huan-Nan Shi, Tao Zhang, Bo-Yan Xi

Abstract

In this paper, using the Schur convexity of the elementary symmetry function and the majorizationinvolving the cyclic moving average proposed by I. Olkin, we establish some new cyclic inequalities whichyield Nesbittís inequality. At the end of the paper, we propose an idea to prove the majorizing relationgiven by I. Olkin using an equivalent relationship between majorization and doubly random matrices.

Mathematics Subject Classfications: 

26D15, 26E60, 26A51

Key words and phrases. 

cyclic moving average; cyclic inequality; Nesbitt's inequality;majorization.

AMEN-A240923.pdf