Cyclic inequalities involving Cater cyclic function

2021/11/24 by Jiajin Wen, Wen, JiaJin, Tianyong Han +3
Mathematics · #26D15 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #G.0 #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2111.15465

openalex publication_date 2021/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By means of the mathematical analysis theory, inequality theory, mathematical induction and the dimension reduction method, under the proper hypotheses, we establish the following cyclic inequalities: ∑_i=1ⁿ a_i^a_n+1-i≤∑_cyc:~n^{1≤ i≤ n} a_i^a_{i + 1}≤ ∑_i=1ⁿ a_i^a_i,~∀ n≥2.

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