Geodesic
New Hermite–Hadamard–Fejér inequalities via k–fractional integrals for differentiable generalized nonconvex functions
Filomat, Tome 34 (2020) no. 8, p. 2549

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DOI

The authors discover a new interesting generalized identity concerning differentiable functions via k–fractional integrals. By using the obtained identity as an auxiliary result, some new estimates with respect to Hermite–Hadamard–Fejér type inequalities via k–fractional integrals for a new class of function involving Raina's function, the so-called generalized (h 1 , h 2)–nonconvex are presented. These inequalities have some connections with known integral inequalities. Also, some new special cases are provided as well from main results.
DOI : 10.2298/FIL2008549K
Classification : 26A51, 26A33, 26D07, 26D10, 26D15
Keywords: Hermite–Hadamard–Fejér inequality, H­­­ölder inequality, power mean inequality, k–fractional integrals 
Artion Kashuri; Themistocles M Rassias. New Hermite–Hadamard–Fejér inequalities via k–fractional integrals for differentiable generalized nonconvex functions. Filomat, Tome 34 (2020) no. 8, p. 2549 . doi: 10.2298/FIL2008549K
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     author = {Artion Kashuri and Themistocles M Rassias},
     title = {New {Hermite{\textendash}Hadamard{\textendash}Fej\'er} inequalities via k{\textendash}fractional integrals for differentiable generalized nonconvex functions},
     journal = {Filomat},
     pages = {2549 },
     year = {2020},
     volume = {34},
     number = {8},
     doi = {10.2298/FIL2008549K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2008549K/}
}
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