Open AccessGeneralized Hermite-Hadamard-Mercer type inequalities via majorization
Author(s) -
Shah Faisal,
Muhammad Adil Khan,
Sajid Iqbal
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202469f
Subject(s) - mathematics , majorization , hadamard transform , hermite polynomials , inequality , pure mathematics , rearrangement inequality , kantorovich inequality , type (biology) , log sum inequality , jensen's inequality , algebra over a field , discrete mathematics , mathematical analysis , linear inequality , convex analysis , convex optimization , regular polygon , geometry , ecology , biology
The Hermite-Hadamard inequality has been recognized as the most pivotal inequality which has grabbed the attention of several mathematicians. In recent years, load of results have been established for this inequality. The main theme of this article is to present generalized Hermite-Hadamard inequality via the Jensen-Mercer inequality and majorization concept. We establish a Hermite-Hadamard inequality of the Jensen-Mercer type for majorized tuples. With the aid of weighted generalized Mercer?s inequality, we also prove a weighted generalized Hermite-Hadamard inequality for certain tuples. The idea of obtaining the results of this paper, may explore a new way for derivation of several other results for Hermite-Hadamard inequality.