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.
References
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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
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.