Open AccessJENSEN–MERCER INEQUALITY AND RELATED RESULTS IN THE FRACTAL SENSE WITH APPLICATIONS
Author(s) -
Saad Ihsan Butt,
Saba Yousaf,
Hijaz Ahmad,
Taher A. Nofal
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x22400084
Subject(s) - mathematics , jensen's inequality , inequality , convex function , regular polygon , function (biology) , log sum inequality , pure mathematics , type (biology) , calculus (dental) , fractal , mathematical analysis , convex analysis , convex optimization , geometry , medicine , ecology , dentistry , evolutionary biology , biology
The most notable inequality pertaining convex functions is Jensen’s inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen’s inequality called as Jensen–Mercer’s inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions. The purpose of this paper is to establish a generalized Jensen–Mercer inequality for a generalized convex function on a real linear fractal set [Formula: see text] ([Formula: see text]. Further, we also demonstrate some generalized Jensen–Mercer-type inequalities by employing local fractional calculus. Lastly, some applications related to Jensen–Mercer inequality and [Formula: see text]-type special means are given. The present approach is efficient, reliable, and may motivate further research in this area.