Some new inequalities of Simpson type for strongly \(\varvec{s}\) -convex func

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• 作者：Jü Hua ; Bo-Yan Xi ; Feng Qi
• 关键词：Simpson type inequality ; Integral identity ; Strongly $$s$$ s ; convex function ; H?lder inequality ; Primary 26D15 ; Secondary 26E60 ; 41A55
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：26
• 期：5-6
• 页码：741-752
• 全文大小：410 KB
• 参考文献：1.Alomari, M., Darus, M., Dragomir, S.S.: New inequalities of simpsons type for s-convex functions with applications, RGMIA Res. Rep. Coll. 12, no. 4, Art. 9. http://?www.?staff.?vu.?edu.?au/?RGMIA/?v12n4.?asp (2009)
  2.Alomari, M.W., Darus, M., Kirmaci, U.S.: Some inequalities of Hermite-Hadamard type for s-convex functions. Acta Math. Sci. Ser. B Engl. Ed. 31(4), 1643-652 (2011). doi:10.-016/?S0252-9602(11)60350-0
  3.Angulo, H., Giménez, J., Moros, A.M., Nikodem, K.: On strongly h-convex functions. Ann. Funct. Anal. 2(2), 85-1 (2011)CrossRef MATH MathSciNet
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  5.Bai, S.-P., Qi, F.: Some inequalities for \((s_1, m_1)\) -\((s_2, m_2)\) -convex functions on the co-ordinates. Glob. J. Math. Anal. 1(1), 22-8 (2013)MathSciNet
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  20.Wang, Y., Wang, S.-H., Qi, F.: Simpson type integral inequalities in which the power of the absolute value of the first derivative of the integrand is s-preinvex. Facta Univ. Ser. Math. Inform. 28(2), 151-59 (2013)
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• 作者单位：Jü Hua (1) (2)
  Bo-Yan Xi (1)
  Feng Qi (3)
  
  1. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, 028043, Inner Mongolia Autonomous Region, China
  2. Erenhot International College, Inner Mongolia Normal University, Erenhot City, 011100, Inner Mongolia Autonomous Region, China
  3. Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City, 300387, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

In the paper, the authors introduce a concept “strongly \(s\)-convex function-and establish a new integral identity. By this integral identity and H?lder’s inequality, the authors obtain some new inequalities of Simpson type for strongly \(s\)-convex functions. Keywords Simpson type inequality Integral identity Strongly \(s\)-convex function H?lder inequality