2014
DOI: 10.1155/2014/254737
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Generalizeds-Convex Functions on Fractal Sets

Abstract: We introduce two kinds of generalized -convex functions on real linear fractal sets R (0 < < 1). And similar to the class situation, we also study the properties of these two kinds of generalized -convex functions and discuss the relationship between them. Furthermore, some applications are given.

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Cited by 7 publications
(2 citation statements)
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“…Other similar improvements on Hermite-Hadamard type inequalities, including an introduction to generalized convex function on fractal sets, can be seen in [20]. For example, a very new study was carried out on the improvement of Hermite-Hadamard type inequalities via generalized convex functions on fractal set, see [21], and we provide the definition of this concept as…”
Section: Respectivelymentioning
confidence: 98%
“…Other similar improvements on Hermite-Hadamard type inequalities, including an introduction to generalized convex function on fractal sets, can be seen in [20]. For example, a very new study was carried out on the improvement of Hermite-Hadamard type inequalities via generalized convex functions on fractal set, see [21], and we provide the definition of this concept as…”
Section: Respectivelymentioning
confidence: 98%
“…Based on Yang's fractal theory, many scholars who are engaged in inequalities research also extend the research of inequalities to fractal sets. A series of definitions such as generalized convex function, 29,30 generalized harmonically convex functions, 31,32 generalized preinvex functions, 33,34 generalized m-convexity, 35 generalized h-convexity, 36,37 and generalized strongly m-convex 38 on fractal sets were introduced successively. And some inequalities for these types of functions were proposed, such as the literature.…”
Section: Introductionmentioning
confidence: 99%