 HERMITE–HADAMARD TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED s-PREINVEX FUNCTIONS AND THEIR GENERALIZATIONWenbing Sun ()
FRACTALS (fractals), 2021, vol. 29, issue 04, 1-16 Abstract: In this paper, the definition of generalized s-preinvex function on Yang’s fractal sets ℠γ(0 < γ ≤ 1) is proposed, and the generalized Hermite–Hadamard’s inequality for this class of functions is established. By using this convexity, some generalized Hermite–Hadamard type integral inequalities with parameters are established. For these inequalities, the absolute values of twice local fractional order derivative of the functions are generalized s-preinvex functions. Some special integral inequalities can be obtained by assigning special values to the obtained inequalities, and two examples are given to illustrate our results. Finally, we propose the applications of the results in numerical integration and error estimation. Keywords: Generalized s-Preinvex Convex Function; Hermite–Hadamard Type Inequalities; Fractal Sets; Local Fractional Integral; Numerical Integration (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:04:n:s0218348x21500985 Ordering information: This journal article can be ordered from DOI: 10.1142/S0218348X21500985 Access Statistics for this article FRACTALS (fractals) is currently edited by Tara Taylor More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd. |
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