期刊论文详细信息
| Abstract and Applied Analysis | |
| Integral Majorization Theorem for Invex Functions | |
| Research Article | |
| N. Rehman1  Adem Kılıçman3  M. Adil Khan2  | |
| [1] Department of Mathematics and Statistics, Allama Iqbal Open University, H-8, Islamabad, Pakistan, aiou.edu.pk;Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan, upesh.edu.pk;Department of Mathematics and Institute of Mathematical Research, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia, upm.edu.my | |
| Others : 1319477 DOI : 10.1155/2014/149735 |
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| received in 2013-12-18, accepted in 2014-02-11, 发布年份 2014 | |
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【 摘 要 】
We obtain some general inequalities and establish integral inequalities of the majorization type for invex functions. We give applications to relative invex functions.
【 授权许可】
CC BY
Copyright © 2014 M. Adil Khan et al. 2014
【 预 览 】
| Files | Size | Format | View |
|---|---|---|---|
| 149735.pdf | 483KB |
【 参考文献 】
- [1]N. S. Barnett, P. Cerone, S. S. Dragomir. (2009). Majorisation inequalities for Stieltjes integrals. Applied Mathematics Letters.22(3):416-421. DOI: 10.1016/j.aml.2008.06.009.
- [2]J. E. Pecaric, F. Proschan, Y. L. Tong. (1992). Convex Functions, Partial Orderings and Statistical Applications. DOI: 10.1016/j.aml.2008.06.009.
- [3]C. P. Niculescu, F. Popovici. (2006). The extension of majorization inequalities within the framework of relative convexity. Journal of Inequalities in Pure and Applied Mathematics.7(1, article 27):1-6. DOI: 10.1016/j.aml.2008.06.009.
- [4]J. Pečarić, S. Abramovich. (1997). On new majorization theorems. Rocky Mountain Journal of Mathematics.27(3):903-911. DOI: 10.1016/j.aml.2008.06.009.
- [5]A. Ben-Israel, B. Mond. (1986). What is invexity?. Journal of the Australian Mathematical Society B.28(1):1-9. DOI: 10.1016/j.aml.2008.06.009.
- [6]M. A. Hanson. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications.80(2):545-550. DOI: 10.1016/j.aml.2008.06.009.
- [7]B. D. Craven. (1981). Duality for generalized convex fractional programs. Generalized Concavity in Optimization and Economics:473-489. DOI: 10.1016/j.aml.2008.06.009.
- [8]M. A. Noor. (2005). Invex equilibrium problems. Journal of Mathematical Analysis and Applications.302(2):463-475. DOI: 10.1016/j.aml.2008.06.009.
- [9]S. K. Mishra, G. Giorgi. (2008). Invexity and Optimization. DOI: 10.1016/j.aml.2008.06.009.
- [10]S. K. Mishra, J. S. Rautela, R. P. Pant. (2010). Optimality and duality in complex minimax optimization under generalized -invexity. Journal of Nonlinear and Convex Analysis.11(2):357-368. DOI: 10.1016/j.aml.2008.06.009.
- [11]S. K. Mishra, N. G. Rueda. (2011). Generalized invexity-type conditions in constrained optimization. Journal of Systems Science and Complexity.24(2):394-400. DOI: 10.1016/j.aml.2008.06.009.
- [12]S. K. Padhan, C. Nahak. (2010). Second order duality for the variational problems under -(,)-invexity. Computers and Mathematics with Applications.60(12):3072-3081. DOI: 10.1016/j.aml.2008.06.009.
- [13]M. Niezgoda, J. Pečarić. (2012). Hardy-Littlewood-Pólya-type theorems for invex functions. Computers and Mathematics with Applications.64(4):518-526. DOI: 10.1016/j.aml.2008.06.009.
- [14]L. Maligranda, J. E. Pecaric, L. E. Persson. (1995). Weighted favard and berwald inequalities. Journal of Mathematical Analysis and Applications.190(1):248-262. DOI: 10.1016/j.aml.2008.06.009.
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