Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional in...

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Published inJournal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 18
Main Authors Butt, Saad Ihsan, Agarwal, Praveen, Yousaf, Saba, Guirao, Juan L. G.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 03.01.2022
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Fractal space
Fractals
Fractional calculus
Generalized harmonic convex function
Harmonic convex function
Inequalities
Jensen-type inequality
Jensen–Mercer inequality
Local fractional derivative
Mathematics
Mathematics and Statistics
Probability density functions
Fractal space
Jensen-type inequality
26A51
26D10
Jensen–Mercer inequality
26A33
Harmonic convex function
25D15
Generalized harmonic convex function
Local fractional derivative
Local fractional integral
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Summary:In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02735-3