Research Article
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New Integral Inequalities for Co-Ordinated Convex Functions

Year 2021, Volume: 2 Issue: 1, 52 - 69, 29.01.2021

Muhamet Emin Özdemir Ahmet Ocak Akdemir Alper Ekinci

Abstract

In this paper, we prove some new integral inequalities for co-ordinated convex functions by
using a new lemma and fairly elementary analysis.

Keywords

Co-ordinated convex functions Hadamard-Type Inequalities Hölder inequality Power mean inequality

References

  • [1] Bakula M.K., Peˇcari´c J., On the Jensen's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 10 (5), 1271-1292, 2006.
  • [2] Özdemir M.E., Set E., Sarıkaya M.Z., Some new Hadamard's type inequalities for co-ordinated m−convex and (alfa,m)−convex functions, Hacettepe Journal of Mathematics and Statistics, 40, 219- 229, 2011.
  • [3] Özdemir M.E., Latif M.A., Akdemir A.O., On some Hadamard-type inequalities for product of two s−convex functions on the co-ordinates, Journal of Inequalities and Applications, 21, 2012.
  • [4] Set E., Sarıkaya M.Z., Akdemir A.O., A new general inequality for double integrals, American Institu of Phsyics (AIP) Conference Proceedings, 1470, 122-125, 2012.
  • [5] Alomari M., Darus M., Hadamard-type inequalities for s−convex functions, International Mathematical Forum, 40(3), 1965-1975, 2008.
  • [6] Özdemir M.E., A.O. Akdemir, On the hadamard type inequalities involving product of two convex functions on the co-ordinates, Tamkang Journal of Mathematics, 46(2), 129-142, 2015.
  • [7] Akdemir A.O., Özdemir M.E., Some Hadamard-type inequalities for co-ordinated P−convex functions and Godunova-Levin functions, American Institu of Phsyics (AIP) Conference Proceedings, 1309, 7- 15, 2010.
  • [8] Özdemir M.E., Latif M.A., Akdemir A.O., On some Hadamard-type inequalities for product of two h−convex functions on the co-ordinates, Turkish Journal of Science, 1(1), 48-58, 2016.
  • [9] Özdemir M.E., Akdemir A.O., Yıldız C., On co-ordinated quasi-convex functions, Czechoslovak Mathematical Journal, 62(4), 889-900, 2012.
  • [10] Alomari M., Darus M., The Hadamard's inequality for s−convex functions of 2−variables, International Journal of Mathematical Analysis, 2(13), 629-638, 2008.
  • [11] Sarıkaya M.Z., Set E., ¨ Ozdemir M.E., Dragomir S.S., New some Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2), 137-152, 2012.
  • [12] Özdemir M.E., Yıldız C., Akdemir A.O., On some new Hadamard-type inequalities for co-ordinated quasi-convex functions, Hacettepe Journal of Mathematics and Statistics, 41(5), 697-707, 2012.
  • [13] Dragomir S.S., On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 5, 775-788, 2001.
  • [14] Hwang D.Y., Tseng K.L., Yang G.S., Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese Journal of Mathematics, 11, 63-73, 2007.
  • [15] Özdemir M.E., Kavurmacı H., Akdemir A.O., Avcı M., Inequalities for convex and s−convex functions on Δ = [a; b] × [c; d] , Journal of Inequalities and Applications, 20, 2012.
  • [16] Bakula M.K., Özdemir M.E., Peˇcari´c J., Hadamard-type inequalities for m−convex and ( ;m)−convex functions, Journal of Inequalities in Pure and Applied Mathematics, 9(4), 96, 2008.
  • [17] Bakula M.K, Peˇcari´c J., Ribibi´c M., Companion inequalities to Jensen's inequality for m−convex and ( ;m)−convex functions, Journal of Inequalities in Pure and Applied Mathematics, 7(5), 194, 2006.
  • [18] Dragomir S.S., Toader G., Some inequalities for m−convex functions, Studia University Babes Bolyai Mathematica, 38(1), 21-28, 1993.
  • [19] Mihe¸san V.G., A Generalization of the Convexity, Seminar of Functional Equations, Approx. and Convex, 1993.
  • [20] Toader G., Some generalization of the convexity, Proceedings of the Colloquium on Approximation and Optimization, 329-338, 1984.
  • [21] Set E., Sardari M., Özdemir M.E., Rooin J., On generalizations of the Hadamard inequality for ( ;m)−convex functions, Research Group in Mathematical Inequalities and Applications, 12(4), 4, 2009.
  • [22] Özdemir M.E., Avcı M., Set E., On some inequalities of Hermite-Hadamard type via m−convexity, Applied Mathematics Letters, 23, 1065-1070, 2010.
  • [23] Toader G., On a generalization of the convexity, Mathematica, 30(53), 83-87, 1988.
  • [24] Dragomir S.S., On some new inequalities of Hermite-Hadamard type for m−convex functions, Tamkang Journal of Mathematics, 33(1), 45-56, 2002.
  • [25] Set E., Özdemir M.E., Dragomir S.S., On the Hermite-Hadamard inequality and other integral in- equalities involving two functions, Journal of Inequalities and Applications, ID 148102, 2010.

Year 2021, Volume: 2 Issue: 1, 52 - 69, 29.01.2021

Muhamet Emin Özdemir Ahmet Ocak Akdemir Alper Ekinci

Abstract

References

  • [1] Bakula M.K., Peˇcari´c J., On the Jensen's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 10 (5), 1271-1292, 2006.
  • [2] Özdemir M.E., Set E., Sarıkaya M.Z., Some new Hadamard's type inequalities for co-ordinated m−convex and (alfa,m)−convex functions, Hacettepe Journal of Mathematics and Statistics, 40, 219- 229, 2011.
  • [3] Özdemir M.E., Latif M.A., Akdemir A.O., On some Hadamard-type inequalities for product of two s−convex functions on the co-ordinates, Journal of Inequalities and Applications, 21, 2012.
  • [4] Set E., Sarıkaya M.Z., Akdemir A.O., A new general inequality for double integrals, American Institu of Phsyics (AIP) Conference Proceedings, 1470, 122-125, 2012.
  • [5] Alomari M., Darus M., Hadamard-type inequalities for s−convex functions, International Mathematical Forum, 40(3), 1965-1975, 2008.
  • [6] Özdemir M.E., A.O. Akdemir, On the hadamard type inequalities involving product of two convex functions on the co-ordinates, Tamkang Journal of Mathematics, 46(2), 129-142, 2015.
  • [7] Akdemir A.O., Özdemir M.E., Some Hadamard-type inequalities for co-ordinated P−convex functions and Godunova-Levin functions, American Institu of Phsyics (AIP) Conference Proceedings, 1309, 7- 15, 2010.
  • [8] Özdemir M.E., Latif M.A., Akdemir A.O., On some Hadamard-type inequalities for product of two h−convex functions on the co-ordinates, Turkish Journal of Science, 1(1), 48-58, 2016.
  • [9] Özdemir M.E., Akdemir A.O., Yıldız C., On co-ordinated quasi-convex functions, Czechoslovak Mathematical Journal, 62(4), 889-900, 2012.
  • [10] Alomari M., Darus M., The Hadamard's inequality for s−convex functions of 2−variables, International Journal of Mathematical Analysis, 2(13), 629-638, 2008.
  • [11] Sarıkaya M.Z., Set E., ¨ Ozdemir M.E., Dragomir S.S., New some Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28(2), 137-152, 2012.
  • [12] Özdemir M.E., Yıldız C., Akdemir A.O., On some new Hadamard-type inequalities for co-ordinated quasi-convex functions, Hacettepe Journal of Mathematics and Statistics, 41(5), 697-707, 2012.
  • [13] Dragomir S.S., On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese Journal of Mathematics, 5, 775-788, 2001.
  • [14] Hwang D.Y., Tseng K.L., Yang G.S., Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese Journal of Mathematics, 11, 63-73, 2007.
  • [15] Özdemir M.E., Kavurmacı H., Akdemir A.O., Avcı M., Inequalities for convex and s−convex functions on Δ = [a; b] × [c; d] , Journal of Inequalities and Applications, 20, 2012.
  • [16] Bakula M.K., Özdemir M.E., Peˇcari´c J., Hadamard-type inequalities for m−convex and ( ;m)−convex functions, Journal of Inequalities in Pure and Applied Mathematics, 9(4), 96, 2008.
  • [17] Bakula M.K, Peˇcari´c J., Ribibi´c M., Companion inequalities to Jensen's inequality for m−convex and ( ;m)−convex functions, Journal of Inequalities in Pure and Applied Mathematics, 7(5), 194, 2006.
  • [18] Dragomir S.S., Toader G., Some inequalities for m−convex functions, Studia University Babes Bolyai Mathematica, 38(1), 21-28, 1993.
  • [19] Mihe¸san V.G., A Generalization of the Convexity, Seminar of Functional Equations, Approx. and Convex, 1993.
  • [20] Toader G., Some generalization of the convexity, Proceedings of the Colloquium on Approximation and Optimization, 329-338, 1984.
  • [21] Set E., Sardari M., Özdemir M.E., Rooin J., On generalizations of the Hadamard inequality for ( ;m)−convex functions, Research Group in Mathematical Inequalities and Applications, 12(4), 4, 2009.
  • [22] Özdemir M.E., Avcı M., Set E., On some inequalities of Hermite-Hadamard type via m−convexity, Applied Mathematics Letters, 23, 1065-1070, 2010.
  • [23] Toader G., On a generalization of the convexity, Mathematica, 30(53), 83-87, 1988.
  • [24] Dragomir S.S., On some new inequalities of Hermite-Hadamard type for m−convex functions, Tamkang Journal of Mathematics, 33(1), 45-56, 2002.
  • [25] Set E., Özdemir M.E., Dragomir S.S., On the Hermite-Hadamard inequality and other integral in- equalities involving two functions, Journal of Inequalities and Applications, ID 148102, 2010.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Muhamet Emin Özdemir 0000-0002-5992-094X

Ahmet Ocak Akdemir 0000-0003-2466-0508

Alper Ekinci 0000-0003-1589-2593

Publication Date January 29, 2021
Published in Issue Year 2021 Volume: 2 Issue: 1

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