SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 3

New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity

Wenjun LİU
Pages
289–297
Publication Date
2013-03-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we establish some new integral inequalities involvingBeta function via (α, m)-convexity and quasi-convexity, respectively.Our results in special cases recapture known results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we establish some new integral inequalities involvingBeta function via (α, m)-convexity and quasi-convexity, respectively.Our results in special cases recapture known results.
📊
Key Findings & Data:In this paper, we establish some new integral inequalities involvingBeta function via (α, m)-convexity and quasi-convexity, respectively.Our results in special cases recapture known results.
💡
Conclusion & Impact:In this paper, we establish some new integral inequalities involvingBeta function via (α, m)-convexity and quasi-convexity, respectively.Our results in special cases recapture known results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hermite’s inequality · Euler Beta function · H¨older’s inequality

Abstract

In this paper, we establish some new integral inequalities involvingBeta function via (α, m)-convexity and quasi-convexity, respectively.Our results in special cases recapture known results.

Özet

-

🔖

Cite This Article

LİU, W. (2013). New Integral Inequalities Via (α,m)-Convexity and Quasi-Convexity. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 3, 289–297. https://ajindex.com/articles/669606

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. M. Alomari and M. Darus, On the Hadamard’s inequality for log-convex functions on the coordinates, J. Inequal. Appl. 2009, Art. ID 283147 13 pp. M. Alomari, M. Darus and S.S. Dragomir, Inequalities of Hermite-Hadamard’s type for functions whose derivatives absolute values are quasi-convex, RGMIA Res. Rep. Coll., 12 (2009),
  2. Supp., No. 14. A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Mat. 28 (1994), no. 1, 7–12.
  3. M. K. Bakula, M. E. ¨ Ozdemir and J. Peˇ cari´ c, Hadamard type inequalities for m-convex and (α, m)-convex functions, JIPAM. J. Inequal. Pure Appl. Math. 9 (2008), no. 4, Article 96, 12 pp. (electronic). M. K. Bakula and J. Peˇ cari´ c, Note on some Hadamard-type inequalities, JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), no. 3, Article 74, 9 pp. (electronic). M. K. Bakula, J. Peˇ cari´ c and M. Ribiˇ ci´ c, Companion Inequalities to Jensen’s Inequality for m-convex and (α, m)-convex Functions, JIPAM. J. Inequal. Pure Appl. Math. 7 (2006), no. 5, Article 194, 15 pp. (electronic). C. Dinu, Hermite-Hadamard inequality on time scales, J. Inequal. Appl. 2008, Art. ID 287947, 24 pp. S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  4. S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), no. 5, 91–95.
  5. S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math. 33 (2002), no. 1, 55–65.
  6. S. S. Dragomir and S. Fitzpatrick, The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Math. 32 (1999), no. 4, 687–696.
  7. P. M. Gill, C. E. M. Pearce and J. Peˇ cari´ c, Hadamard’s inequality for r-convex functions, J. Math. Anal. Appl. 215 (1997), no. 2, 461–470.
  8. V. N. Huy and N. T. Chung, Some generalizations of the Fej´ er and Hermite-Hadamard inequalities in H¨ older spaces, J. Appl. Math. Inform. 29 (2011), no. 3-4, 859–868.
  9. D. A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, An. Univ. Craiova Ser. Mat. Inform. 34 (2007), 83–88.
  10. U. S. Kirmaci et al., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput. 193 (2007), no. 1, 26–35.
  11. Z. Liu, Generalization and improvement of some Hadamard type inequalities for Lipschitzian mappings, J. Pure Appl. Math. Adv. Appl. 1 (2009), no. 2, 175–181. D