Hermite-hadamard type ınequalities for multiplicatively s-convex functions

Serap Özcan

doi:10.17776/csj.663559

Research Article

Hermite-hadamard type ınequalities for multiplicatively s-convex functions

Year 2020, Volume: 41 Issue: 1, 245 - 259, 22.03.2020

Serap Özcan

https://doi.org/10.17776/csj.663559

Cited By: 16

https://izlik.org/JA36UW76AG

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

Serap Özcan

https://doi.org/10.17776/csj.663559

Cited By: 16

https://izlik.org/JA36UW76AG

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	Serap Özcan 0000-0001-6496-5088
Project Number	KLUBAP-191
Submission Date	December 23, 2019
Acceptance Date	February 24, 2020
Publication Date	March 22, 2020
DOI	https://doi.org/10.17776/csj.663559
IZ	https://izlik.org/JA36UW76AG
Published in Issue	Year 2020 Volume: 41 Issue: 1

Cite

APA	Özcan, S. (2020). Hermite-hadamard type ınequalities for multiplicatively s-convex functions. Cumhuriyet Science Journal, 41(1), 245-259. https://doi.org/10.17776/csj.663559