In this paper by using the concept of log-η-convexity of functions some interesting inequalities are investigated. In fact new Hermite-Hadamard type integral inequalities involving log-η-convex function are established. The obtained results have as particular cases those previously obtained for log-convex
| Published in | Mathematics and Computer Science (Volume 1, Issue 4) |
| DOI | 10.11648/j.mcs.20160104.13 |
| Page(s) | 86-92 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2016. Published by Science Publishing Group |
Log-η-Convex Functions, Integral Inequalities, Hermite-Hadamard Type Inequalities
| [1] | R. Ahlswede and D. E. Daykin, Integrals inequalities for increasing functions, Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 86(3)( 1979), 391–394. |
| [2] | A. Aleman, On some generalizations of convex sets and convex functions, Anal. Numer. Theor. Approx. 14 (1985), 1-6. |
| [3] | C. R. Bector and C. Singh, B-Vex functions, J. Optim. Theory. Appl. 71(2) (1991), 237-253. |
| [4] | S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite–Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, (2000). |
| [5] | B. Definetti, Sulla stratificazioni convesse, Ann. Math. Pura. Appl. 30 (1949), 173-183. |
| [6] | M. Eshaghi Gordji, S. S. Dragomir and M. Rostamian Delavar, An inequality related to η-convex functions (II), Int. J. Nonlinear Anal. Appl. 6(2) (2015), 26-32. |
| [7] | M. Eshaghi Gordji, M. Rostamian Delavar and M. De La Sen, On φ-convex functions, J. Math. Inequal. 10(1) (2016), 173-183. |
| [8] | M. Eshaghi Gordji, M. Rostamian Delavar and S. S. Dragomir, Some inequalities related to η-convex functions, Preprint, RGMIA Res. Rep. Coll. 18(2015), Art. 08. [Online http://rgmia.org/papers/v18/v18a08.pdf]. |
| [9] | M. Eshaghi, F. Sajadian and M. Rostamian Delavar, Inequalities for log-η-convex functions, to apear in Int. J. Nonlinear Anal. Appl. |
| [10] | M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981), 545-550. |
| [11] | D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), 821-828. |
| [12] | I. Hsu and R. G. Kuller, Convexity of vector-valued functions, Proc. Amer. Math. Soc. 46 (1974), 363-366. |
| [13] | J. L. W. V. Jensen, On konvexe funktioner og uligheder mellem middlvaerdier, Nyt. Tidsskr. Math. B. 16 (1905), 49-69. |
| [14] | D. Kuroiwa, Convexity for set-valued maps, Appl. Math. Lett. 9 (1996), 97-101. |
| [15] | R. B. Manfrino, R. V. Delgado and J.A.G. Ortega, Inequalities a Mathematical Olympiad Approach, Birkha ̈user, (2009). |
| [16] | O. L. Mangasarian, Pseudo-convex functions, SIAM Journal on Control, 3 (1965), 281-290. |
| [17] | D. S. Mitrinovic´, J. E. Pecˇaric´, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, (1993). |
| [18] | J. E. Pecaric, F. Proschan and Y. L. Tong, Convex functions, partial orderings and statistical applications, Academic Press, Boston, (1992). |
| [19] | B. T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. 7 (1966), 72-75. |
| [20] | T. Rajba, On strong delta-convexity and Hermite-Hadamard type inequalities for delta-convex functions of higher order, Math. Inequal. Appl. 18(1) (2015), 267-293. |
| [21] | M. Rostamian Delavar and S. S. Dragomir, On η-convexity, to appear in Math. Inequal. Appl. |
| [22] | S. Varosanec, On h-convexity, J. Math. Anal. Appl. 326(1) (2007), 303-311. |
| [23] | X. M. Yang, E-convex sets, E-convex functions and E-convex programming, J. Optim. Theory. Appl. 109 (2001), 699-704. |
APA Style
Mohsen Rostamian Delavar, Farhad Sajadian. (2016). Hermite-Hadamard Type Integral Inequalities for Log-η-Convex Functions. Mathematics and Computer Science, 1(4), 86-92. https://doi.org/10.11648/j.mcs.20160104.13
ACS Style
Mohsen Rostamian Delavar; Farhad Sajadian. Hermite-Hadamard Type Integral Inequalities for Log-η-Convex Functions. Math. Comput. Sci. 2016, 1(4), 86-92. doi: 10.11648/j.mcs.20160104.13
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Download@article{10.11648/j.mcs.20160104.13,
author = {Mohsen Rostamian Delavar and Farhad Sajadian},
title = {Hermite-Hadamard Type Integral Inequalities for Log-η-Convex Functions},
journal = {Mathematics and Computer Science},
volume = {1},
number = {4},
pages = {86-92},
doi = {10.11648/j.mcs.20160104.13},
url = {https://doi.org/10.11648/j.mcs.20160104.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160104.13},
abstract = {In this paper by using the concept of log-η-convexity of functions some interesting inequalities are investigated. In fact new Hermite-Hadamard type integral inequalities involving log-η-convex function are established. The obtained results have as particular cases those previously obtained for log-convex},
year = {2016}
}
TY - JOUR T1 - Hermite-Hadamard Type Integral Inequalities for Log-η-Convex Functions AU - Mohsen Rostamian Delavar AU - Farhad Sajadian Y1 - 2016/11/09 PY - 2016 N1 - https://doi.org/10.11648/j.mcs.20160104.13 DO - 10.11648/j.mcs.20160104.13 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 86 EP - 92 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20160104.13 AB - In this paper by using the concept of log-η-convexity of functions some interesting inequalities are investigated. In fact new Hermite-Hadamard type integral inequalities involving log-η-convex function are established. The obtained results have as particular cases those previously obtained for log-convex VL - 1 IS - 4 ER -
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