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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 4

ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS

Mevlüt TUNÇ
Çetin YILDIZ
Alper EKİNCİ
Sayfa
309–317
Yayın Tarihi
2013-04-01
DOI
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Also we give some sophisticated results for some different kinds of convex functions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we prove some new inequalities of Simpson’s type for functions whose derivatives of absolute values are h−convex and h−concavefunctions.
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Temel Bulgular & Veri:Some new estimations are obtained.
💡
Sonuç & Katkı:Also we give some sophisticated results for some different kinds of convex functions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:h−convex and h−concave functions · Simpson’s Inequality · H¨older Inequality.

Abstract

In this paper, we prove some new inequalities of Simpson’s type for functions whose derivatives of absolute values are h−convex and h−concavefunctions. Some new estimations are obtained. Also we give some sophisticated results for some different kinds of convex functions.

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Bu Makaleye Atıf Yap

TUNÇ, M., YILDIZ, Ç., EKİNCİ, A. (2013). ON SOME INEQUALITIES OF SIMPSON’S TYPE VIA h−CONVEX FUNCTIONS. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 4, 309–317. https://ajindex.com/articles/669595

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Kaynakça (8)

  1. Sarıkaya, M. Z., Set, E., and ¨ Ozdemir, M. E., On new inequalities of Simpson’s type for convex functions, RGMIA Res. Rep. Coll., 13 (2), Art. 2, 2010.
  2. Dragomir, S. S., Agarwal, R. P. and Cerone, P., On Simpson’s inequality and applications, J. of Ineq. and Appl., 5, 533–579, 2000.
  3. Alomari, M., Darus, M. and Dragomir, S. S., New inequalities of Simpson’s type for s−convex functions with applications, RGMIA Res. Rep. Coll., 12 (4), Article 9, 2009.
  4. Dragomir, S. S., Peˇ cari´ c, J. and Persson, L. E. Some inequalities of Hadamard type, Soochow J.Math. 21, 335–341, 1995. Godunova,E. K. and Levin, V. I. Neravenstva dlja funkcii ˇ sirokogo klassa, soderˇ zaˇ scego vypuklye, monotonnye i nekotorye drugie vidy funkcii, in: Vycislitel. Mat. i. Mat. Fiz. Meˇ zvuzov. Sb. Nauc. Trudov, MGPI, Moskva, pp. 138–142, 1985.
  5. Hudzik, H. and Maligranda, L. Some remarks on s−convex functions, Aequationes Math. 48, 100–111, 1994. Varoˇ sanec, S. On h−convexity, J. Math. Anal. Appl., 326, 303–311, 2007.
  6. Breckner, W. W. Stetigkeitsaussagen f¨ ur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23, 13–20, 1978.
  7. Breckner, W. W. Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Numer. Thkor. Approx., 22, 39–51, 1993.
  8. Sarıkaya, M. Z., Sa˘ glam, A. and Yıldırım, H.,On some Hadamard-type inequalities for h−convex functions, Journal of Mathematical Inequalities, 2 (3), 335–341, 2008.