Research Article
Year 2020,
Volume: 41 Issue: 1, 245 - 259, 22.03.2020
Abstract
In this paper, some integral inequalities of Hermite-Hadamard type for multiplicatively s-convex functions are obtained. Also, some new inequalities involving multiplicative integrals are established for product and quotient of convex and multiplicatively s-convex functions.
Keywords
Convex functions multiplicatively s-convex functions multiplicative calculus Hermite-Hadamard inequalities
Project Number
KLUBAP-191
References
- [1] Dragomir, S. S. and Pearce, C. E. M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
- [2] Pecaric, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings and statistical applications, Academic Press, Boston, 1992.
- [3] Dragomir, S. S., Pecaric, J. and Persson, L. E., Some inequalities of Hadamard type, Soochow J. Math., 21(3) (1995) 335-341.
- [4] İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Stat., 43(6) (2014) 935-942.
- [5] Kadakal, H., Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Science Journal, 40 (3) (2019) 670-678.
- [6] Kadakal, H., Kadakal, M. and İşcan, İ., Some new integral inequalities for n-times differentiable s-convex and s-concave functions in the second sense, Mathematics and Statistics, 5(2) (2017) 94-98.
- [7] Latif, M. A., Dragomir, S. S. and Momoniat, E., New inequalities of Hermite-Hadamard type for n-times differentiable s-convex functions with applications, Int. J. Anal. Appl., 13 (2) (2017) 119-131.
- [8] Noor, M. A., Qi, F. and Awan, M. U., Some Hermite-Hadamard type inequalities for log-h-convex functions, Analysis, 33 (2013) 1-9.
- [9] Özcan, S., Some integral inequalities for harmonically (α,s)-convex functions, J. Func. Spaces, Vol. 2019 (2019), Article ID 2394021, 8 pages.
- [10] Özcan, S. and İşcan, İ., Some New Hermite-Hadamard type inequalities for s-convex functions and their applications, J. Ineq. Appl., Article number: 2019:201 (2019).
- [11] Özdemir, M. E., Ardıç, M. A. and Önalan, H. K., Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals, Turkish Journal of Science, 1 (1) (2016) 28-40.
- [12] Sarıkaya, M. Z. and Budak, H., Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat, 30 (5) (2016) 1315-1326.
- [13] Set, E., İşcan, İ., Sarıkaya, M. Z. and Özdemir, M. E., On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals, Appl. Math. Comp., 259 (2015) 875-881.
- [14] Bashirov, A. E., Kurpınar, E. M. and Özyapıcı, A., Multiplicative calculus and applications, J. Math. Anal. Appl., 337(1) (2008) 36-48.
- [15] Ali, M. A., Abbas, M., Zhang, Z., Sial, I. B. and Arif, R., On integral inequalities for product and quotient of two multiplicatively convex functions, Asian Research J. Math., 12(3) (2019) 1-11.
- [16] Dragomir, S. S. and Pearce, C. E. M., Quasi-convex functions and Hermite-Hadamard’s inequality, Bull. Austral. Math. Soc., 57 (1998) 377-385.
- [17] Hudzik, H., Maligranda, L., Some remarks on s-convex functions, Aequ. Math., 48(1) (1994), 100-111.
- [18] Dragomir, S.S., Fitzpatrick, S., The Hadamard inequalities for s-convex functions in the second sense, Demonstr. Math., 32(4) (1999) 687-696.
- [19] Xi, B.-Y. and Qi, F., Some integral inequalities of Hermite-Hadamard type for s-logarithmically convex functions, Acta Mathematica Scientis, English Series, 35A(3) (2015) 515-526.
Year 2020,
Volume: 41 Issue: 1, 245 - 259, 22.03.2020
Abstract
Supporting Institution
Kırklareli Üniversitesi Bilimsel Araştırma Projeleri Koordinatörlüğü
Project Number
KLUBAP-191
References
- [1] Dragomir, S. S. and Pearce, C. E. M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
- [2] Pecaric, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings and statistical applications, Academic Press, Boston, 1992.
- [3] Dragomir, S. S., Pecaric, J. and Persson, L. E., Some inequalities of Hadamard type, Soochow J. Math., 21(3) (1995) 335-341.
- [4] İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Stat., 43(6) (2014) 935-942.
- [5] Kadakal, H., Hermite-Hadamard type inequalities for two times differentiable arithmetic-harmonically convex functions, Cumhuriyet Science Journal, 40 (3) (2019) 670-678.
- [6] Kadakal, H., Kadakal, M. and İşcan, İ., Some new integral inequalities for n-times differentiable s-convex and s-concave functions in the second sense, Mathematics and Statistics, 5(2) (2017) 94-98.
- [7] Latif, M. A., Dragomir, S. S. and Momoniat, E., New inequalities of Hermite-Hadamard type for n-times differentiable s-convex functions with applications, Int. J. Anal. Appl., 13 (2) (2017) 119-131.
- [8] Noor, M. A., Qi, F. and Awan, M. U., Some Hermite-Hadamard type inequalities for log-h-convex functions, Analysis, 33 (2013) 1-9.
- [9] Özcan, S., Some integral inequalities for harmonically (α,s)-convex functions, J. Func. Spaces, Vol. 2019 (2019), Article ID 2394021, 8 pages.
- [10] Özcan, S. and İşcan, İ., Some New Hermite-Hadamard type inequalities for s-convex functions and their applications, J. Ineq. Appl., Article number: 2019:201 (2019).
- [11] Özdemir, M. E., Ardıç, M. A. and Önalan, H. K., Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals, Turkish Journal of Science, 1 (1) (2016) 28-40.
- [12] Sarıkaya, M. Z. and Budak, H., Generalized Hermite-Hadamard type integral inequalities for fractional integrals, Filomat, 30 (5) (2016) 1315-1326.
- [13] Set, E., İşcan, İ., Sarıkaya, M. Z. and Özdemir, M. E., On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals, Appl. Math. Comp., 259 (2015) 875-881.
- [14] Bashirov, A. E., Kurpınar, E. M. and Özyapıcı, A., Multiplicative calculus and applications, J. Math. Anal. Appl., 337(1) (2008) 36-48.
- [15] Ali, M. A., Abbas, M., Zhang, Z., Sial, I. B. and Arif, R., On integral inequalities for product and quotient of two multiplicatively convex functions, Asian Research J. Math., 12(3) (2019) 1-11.
- [16] Dragomir, S. S. and Pearce, C. E. M., Quasi-convex functions and Hermite-Hadamard’s inequality, Bull. Austral. Math. Soc., 57 (1998) 377-385.
- [17] Hudzik, H., Maligranda, L., Some remarks on s-convex functions, Aequ. Math., 48(1) (1994), 100-111.
- [18] Dragomir, S.S., Fitzpatrick, S., The Hadamard inequalities for s-convex functions in the second sense, Demonstr. Math., 32(4) (1999) 687-696.
- [19] Xi, B.-Y. and Qi, F., Some integral inequalities of Hermite-Hadamard type for s-logarithmically convex functions, Acta Mathematica Scientis, English Series, 35A(3) (2015) 515-526.
There are 19 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Project Number | KLUBAP-191 |
| Publication Date | March 22, 2020 |
| Submission Date | December 23, 2019 |
| Acceptance Date | February 24, 2020 |
| Published in Issue | Year 2020 Volume: 41 Issue: 1 |