A dimensionality reduction principle on the optimization of function

Abstract

Abstract. In this paper, we put out a dimensionality reduction principle on the optimization of function, in other words, we show that inf a∈R nunder the proper hypotheses. As applications, we study the optimal problems of linear inequalities involving function power means. In order to show the significance of our results, we give an example for a discrete case by means of the software Mathematica and another example involving space science.Mathematics subject classification (2010): 26D15, 26E60.

Cyclic inequalities involving Cater cyclic function

“…The proof method of Theorem 1.2 is called the dimensionality reduction method. The relevant literatures on proving inequalities by means of the dimensionality reduction method can be see [2,3,5,7]. The dimension reduction process of the proof is as follows.…”

“…In this paper, we will study the lower with upper bounds of the Cater cyclic function and establish two Cater-type cyclic inequalities, and display the applications of the dimension reduction method [2,3,5,7] in the inequality theory.…”