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Integral Inequalities for Different Kinds of Convexity via Classical Inequalities

Year 2020, Volume: 5 Issue: 3, 305 - 313, 30.12.2020
https://izlik.org/JA92TA66ZN

Abstract

In this study, we obtain some new integral inequalities for different classes of convex functions by using classical inequalities like general Cauchy inequality and reverse Minkowski inequality.

References

  • M.K. Bakula, M.E. Özdemir and J. Peµcaric, Hadamard-type inequalities for m-convex and (α; m)convex functions, J. Inequal. Pure and Appl. Math., 9, (4), (2007), Article 96.
  • M.K. Bakula, J. Peµcaric and M. Ribibic, Companion inequalities to Jensen's inequality for m-convex and (α; m)convex functions, J. Inequal. Pure and Appl. Math., 7 (5) (2006), Article 194.
  • S.S. Dragomir and G. Toader, Some inequalities for mconvex functions, Studia University Babes Bolyai, Mathematica, 38 (1) (1993), 21-28.
  • V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
  • G. Toader, Some generalization of the convexity, Proc. Colloq. Approx. Opt., Cluj-Napoca, (1984), 329-338.
  • E. Set, M. Sardari, M.E. Ozdemir and J. Rooin, On generalizations of the Hadamard inequality for (α; m)convex functions, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 4.
  • M.E. Özdemir, M. Avcı and E. Set, On some inequalities of Hermite-Hadamard type via m-convexity, Applied Mathematics
  • G. Toader, On a generalization of the convexity, Mathematica, 30 (53) (1988), 83-87.
  • S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for mconvex functions, Tamkang Journal of Mathematics, 33 (1) (2002).
  • H. Hudzik and L. Maligranda, Some remarks on sconvex functions, Aequationes Math., 48 (1994) 100-111.
  • W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978) 13-20.
  • W.W. Breckner, Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Number. Theor. Approx., 22 (1993) 39-51.
  • S. Hussain, M.I. Bhatti and M. Iqbal, Hadamard-type inequalities for sconvex functions, Punjab University, Journal of Mathematics, 41 (2009) 51-60.
  • S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math., 32 (4) (1999) 687-696.
  • U.S. Kırmacı, M.K. Bakula, M.E. Özdemir and J. Peµcaric, Hadamard-type inequalities for s-convex functions, Applied Mathematics and Computation, 193 (2007) 26-35.
  • L. Bougofa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 2, article 60, 2006.
  • Q.A. Ngo, D.D. Thang, T.T. Dat and D.A. Tuan, Notes on an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 4, article 120, 2

Year 2020, Volume: 5 Issue: 3, 305 - 313, 30.12.2020
https://izlik.org/JA92TA66ZN

Abstract

References

  • M.K. Bakula, M.E. Özdemir and J. Peµcaric, Hadamard-type inequalities for m-convex and (α; m)convex functions, J. Inequal. Pure and Appl. Math., 9, (4), (2007), Article 96.
  • M.K. Bakula, J. Peµcaric and M. Ribibic, Companion inequalities to Jensen's inequality for m-convex and (α; m)convex functions, J. Inequal. Pure and Appl. Math., 7 (5) (2006), Article 194.
  • S.S. Dragomir and G. Toader, Some inequalities for mconvex functions, Studia University Babes Bolyai, Mathematica, 38 (1) (1993), 21-28.
  • V.G. Mihe¸san, A generalization of the convexity, Seminar of Functional Equations, Approx. and Convex, Cluj-Napoca (Romania) (1993).
  • G. Toader, Some generalization of the convexity, Proc. Colloq. Approx. Opt., Cluj-Napoca, (1984), 329-338.
  • E. Set, M. Sardari, M.E. Ozdemir and J. Rooin, On generalizations of the Hadamard inequality for (α; m)convex functions, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 4.
  • M.E. Özdemir, M. Avcı and E. Set, On some inequalities of Hermite-Hadamard type via m-convexity, Applied Mathematics
  • G. Toader, On a generalization of the convexity, Mathematica, 30 (53) (1988), 83-87.
  • S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for mconvex functions, Tamkang Journal of Mathematics, 33 (1) (2002).
  • H. Hudzik and L. Maligranda, Some remarks on sconvex functions, Aequationes Math., 48 (1994) 100-111.
  • W.W. Breckner, Stetigkeitsaussagen fur eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math., 23 (1978) 13-20.
  • W.W. Breckner, Continuity of generalized convex and generalized concave set-valued functions, Rev Anal. Number. Theor. Approx., 22 (1993) 39-51.
  • S. Hussain, M.I. Bhatti and M. Iqbal, Hadamard-type inequalities for sconvex functions, Punjab University, Journal of Mathematics, 41 (2009) 51-60.
  • S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math., 32 (4) (1999) 687-696.
  • U.S. Kırmacı, M.K. Bakula, M.E. Özdemir and J. Peµcaric, Hadamard-type inequalities for s-convex functions, Applied Mathematics and Computation, 193 (2007) 26-35.
  • L. Bougofa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 2, article 60, 2006.
  • Q.A. Ngo, D.D. Thang, T.T. Dat and D.A. Tuan, Notes on an integral inequality, Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 4, article 120, 2
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Alper Ekinci 0000-0003-1589-2593

Ahmet Ocak Akdemir 0000-0003-2466-0508

Muhamet Emin Özdemir 0000-0002-5992-094X

Publication Date December 30, 2020
IZ https://izlik.org/JA92TA66ZN
Published in Issue Year 2020 Volume: 5 Issue: 3

Cite

APA Ekinci, A., Akdemir, A. O., & Özdemir, M. E. (2020). Integral Inequalities for Different Kinds of Convexity via Classical Inequalities. Turkish Journal of Science, 5(3), 305-313. https://izlik.org/JA92TA66ZN
AMA 1.Ekinci A, Akdemir AO, Özdemir ME. Integral Inequalities for Different Kinds of Convexity via Classical Inequalities. TJOS. 2020;5(3):305-313. https://izlik.org/JA92TA66ZN
Chicago Ekinci, Alper, Ahmet Ocak Akdemir, and Muhamet Emin Özdemir. 2020. “Integral Inequalities for Different Kinds of Convexity via Classical Inequalities”. Turkish Journal of Science 5 (3): 305-13. https://izlik.org/JA92TA66ZN.
EndNote Ekinci A, Akdemir AO, Özdemir ME (December 1, 2020) Integral Inequalities for Different Kinds of Convexity via Classical Inequalities. Turkish Journal of Science 5 3 305–313.
IEEE [1]A. Ekinci, A. O. Akdemir, and M. E. Özdemir, “Integral Inequalities for Different Kinds of Convexity via Classical Inequalities”, TJOS, vol. 5, no. 3, pp. 305–313, Dec. 2020, [Online]. Available: https://izlik.org/JA92TA66ZN
ISNAD Ekinci, Alper - Akdemir, Ahmet Ocak - Özdemir, Muhamet Emin. “Integral Inequalities for Different Kinds of Convexity via Classical Inequalities”. Turkish Journal of Science 5/3 (December 1, 2020): 305-313. https://izlik.org/JA92TA66ZN.
JAMA 1.Ekinci A, Akdemir AO, Özdemir ME. Integral Inequalities for Different Kinds of Convexity via Classical Inequalities. TJOS. 2020;5:305–313.
MLA Ekinci, Alper, et al. “Integral Inequalities for Different Kinds of Convexity via Classical Inequalities”. Turkish Journal of Science, vol. 5, no. 3, Dec. 2020, pp. 305-13, https://izlik.org/JA92TA66ZN.
Vancouver 1.Ekinci A, Akdemir AO, Özdemir ME. Integral Inequalities for Different Kinds of Convexity via Classical Inequalities. TJOS [Internet]. 2020 Dec. 1;5(3):305-13. Available from: https://izlik.org/JA92TA66ZN