Moroccan Journal of Pure and Applied Analysis (May 2021)

Generalized functional inequalities in Banach spaces

  • Dimou H.,
  • Aribou Y.,
  • Kabbaj S.

DOI
https://doi.org/10.2478/mjpaa-2021-0022
Journal volume & issue
Vol. 7, no. 2
pp. 337 – 349

Abstract

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In this paper, we solve and investigate the generalized additive functional inequalities ‖F(∑i=1nxi)-∑i=1nF(xi)‖≤‖F(1n∑i=1nxi)-1n∑i=1nF(xi)‖\left\| {F\left( {\sum\limits_{i = 1}^n {{x_i}} } \right) - \sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\| \le \left\| {F\left( {{1 \over n}\sum\limits_{i = 1}^n {{x_i}} } \right) - {1 \over n}\sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\| and ‖F(1n∑i=1nxi)-1n∑i=1nF(xi)‖≤‖F(∑i=1nxi)-∑i=1nF(xi)‖.\left\| {F\left( {{1 \over n}\sum\limits_{i = 1}^n {{x_i}} } \right) - {1 \over n}\sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\| \le \left\| {F\left( {\sum\limits_{i = 1}^n {{x_i}} } \right) - \sum\limits_{i = 1}^n {F\left( {{x_i}} \right)} } \right\|.

Keywords