On approximately Convex and Affine Sequences

2024/04/18 by Angshuman R. Goswami, Goswami, Angshuman Robin
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #General Mathematics (math.GM) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2406.15380

openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, our primary objective is to study a possible decomposition of an approximately convex sequence. For a given ε>0; a sequence _n=0^∞ is said to be ε-convex, if for any i,j∈ℕ with i_n=0^∞ satisfies the following form of inequality |(u_i-u_i-1)-(u_j-u_j-1)|≤\dfracεn-i \quadfor some n∈]i,j]∩ℕ; then we term it as ε-affine sequence. Such a sequence can be decomposed as the algebraic summation of an affine and a bounded sequence whose supremum norm doesn't exceed ε.

Related

• Decomposition of Approximately Monotone and Convex Sequences
• On Characterizations of Convex and Approximately Subadditive Sequences
• On approximately convex and affine functions
• On Relative Convex Sequences
• Ubiquitous algorithms in convex optimization generate self-contracted sequences