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Year 2019, Volume: 68 Issue: 2, 1556 - 1575, 01.08.2019

Zeynep Şanlı Tuncay Köroğlu Mehmet Kunt

https://doi.org/10.31801/cfsuasmas.413019
Cited By: 1

Abstract

References

  • Abbas, G. and Farid, G., Hadamard and Fejer-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals, J. Anal., 25(1) (2017), 107-119.
  • Abbas, G., Farid, G., Khan, K. A. and Rehman, A. U., Generalized fractional integrals inequalities for harmonically convex function, J. Anal., 8(4) (2017), 1-16.
  • Awan, M. U., Noor, M. A., Mihai, M. V. and Noor, K. I., Inequalities via harmonic convex functions: Conformable fractional calculus approach, J. Math. Inequal., 12(1) (2018), 143-153.
  • Chen, H. and Katugampola, U. N., Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for generalized fractional integrals. J. Math. Anal. Appl., 446, (2017) 1274--1291.
  • Chen, F. and Wu, S., Fejer and Hermite-Hadamard type inequalities for harmonically convex functions, J. Appl. Math., Article ID:386806 (2014), 1-6.
  • Dragomir, S. S., Inequalities of Hermite-Hadamard type for HA-convex functions, Moroccan J. P. Appl. Anal., 3(1) (2017), 83-101.
  • İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Statist., 46(6) (2014), 935-942.
  • İşcan, İ., Kunt, M. and Yazıcı, N., Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integrals, New Trends in Math. Sci., 4(3) (2016), 239-253.
  • İşcan, İ. and Wu, S., Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014), 237-244.
  • Katugampola, U. N., New approach to generalized fractional integral, Appl. Math. Comput., 218(3) (2011) 860-865.
  • Katugampola, U. N., Mellin transforms of generalized fractional integrals and derivatives, Appl. Math. Comput., 257 (2015) 566-580.
  • Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006.
  • Kunt, M. and İşcan, İ., Hermite-Hadamard type inequalities for harmonically (α,m)-convex functions by using fractional integrals, Konuralp J. Math., 5(1) (2017), 201-213.
  • Kunt, M., İşcan, İ. and Yazıcı, N., Hermite-Hadamard type inequalities for product of harmonically convex functions via Riemann-Liouville fractional integrals, J. Math. Anal., 7(4) (2016), 74-82.
  • Kunt, M., İşcan, İ., Yazıcı, N. and Gözütok, U., On new inequalities of Hermite-Hadamard-Fejer type for harmonically convex functions via fractional integrals, Springer Plus, 5(635) (2016), 1-19.
  • Mihai, M. V., Awan, M. U., Noor, M. A. and Noor, K. I., Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function, J. Inequal. Appl., 265 (2017), 1-13.
  • Mumcu, İ., Set, E. and Akdemir, A. O., Hermite-Hadamard type inequalities for harmonically convex functions via Katuganpola fractional integrals, Researchgate Preprint, (2017), Available online from: https://www.researchgate.net/publication/319649734.
  • Prudnikov, A. P., Brychkov, Y. A. and Marichev, O. J., Integral and series, Elementary Functions, vol. 1, Nauka, Moscow, 1981.
  • Roberts, A. W. and Varberg, D. E., Convex functions, Academic Press, New York, 1973.
  • Şanlı, Z., Kunt, M. and Köroğlu, T., New Riemann-Liouville fractional Hermite Hadamard type inequalities for harmonically convex functions, ResearchGate Preprint, 2018, Doi: 10.13140/RG.2.2.14263.42400.

Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

Year 2019, Volume: 68 Issue: 2, 1556 - 1575, 01.08.2019

Zeynep Şanlı Tuncay Köroğlu Mehmet Kunt

https://doi.org/10.31801/cfsuasmas.413019
Cited By: 1

Abstract




In this paper,we proved three new Katugampola fractional Hermite-
Hadamard type inequalities for harmonically convex functions by using the left
and the right fractional integrals independently. One of our Katugampola frac-
tional Hermite-Hadamard type inequalities is better than given in [15]. Also,
we gave two new Katugampola fractional identities for differentiable functions.
By using these identities, we obtained some new trapezoidal type inequalities
for harmonically convex functions. Our results generalize many results from
earlier papers. 




Keywords

Harmonically convex functions Hermite-Hadamard inequalities Katugampola fractional integrals

References

  • Abbas, G. and Farid, G., Hadamard and Fejer-Hadamard type inequalities for harmonically convex functions via generalized fractional integrals, J. Anal., 25(1) (2017), 107-119.
  • Abbas, G., Farid, G., Khan, K. A. and Rehman, A. U., Generalized fractional integrals inequalities for harmonically convex function, J. Anal., 8(4) (2017), 1-16.
  • Awan, M. U., Noor, M. A., Mihai, M. V. and Noor, K. I., Inequalities via harmonic convex functions: Conformable fractional calculus approach, J. Math. Inequal., 12(1) (2018), 143-153.
  • Chen, H. and Katugampola, U. N., Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for generalized fractional integrals. J. Math. Anal. Appl., 446, (2017) 1274--1291.
  • Chen, F. and Wu, S., Fejer and Hermite-Hadamard type inequalities for harmonically convex functions, J. Appl. Math., Article ID:386806 (2014), 1-6.
  • Dragomir, S. S., Inequalities of Hermite-Hadamard type for HA-convex functions, Moroccan J. P. Appl. Anal., 3(1) (2017), 83-101.
  • İşcan, İ., Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe J. Math. Statist., 46(6) (2014), 935-942.
  • İşcan, İ., Kunt, M. and Yazıcı, N., Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integrals, New Trends in Math. Sci., 4(3) (2016), 239-253.
  • İşcan, İ. and Wu, S., Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014), 237-244.
  • Katugampola, U. N., New approach to generalized fractional integral, Appl. Math. Comput., 218(3) (2011) 860-865.
  • Katugampola, U. N., Mellin transforms of generalized fractional integrals and derivatives, Appl. Math. Comput., 257 (2015) 566-580.
  • Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., Theory and applications of fractional differential equations. Elsevier, Amsterdam, 2006.
  • Kunt, M. and İşcan, İ., Hermite-Hadamard type inequalities for harmonically (α,m)-convex functions by using fractional integrals, Konuralp J. Math., 5(1) (2017), 201-213.
  • Kunt, M., İşcan, İ. and Yazıcı, N., Hermite-Hadamard type inequalities for product of harmonically convex functions via Riemann-Liouville fractional integrals, J. Math. Anal., 7(4) (2016), 74-82.
  • Kunt, M., İşcan, İ., Yazıcı, N. and Gözütok, U., On new inequalities of Hermite-Hadamard-Fejer type for harmonically convex functions via fractional integrals, Springer Plus, 5(635) (2016), 1-19.
  • Mihai, M. V., Awan, M. U., Noor, M. A. and Noor, K. I., Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function, J. Inequal. Appl., 265 (2017), 1-13.
  • Mumcu, İ., Set, E. and Akdemir, A. O., Hermite-Hadamard type inequalities for harmonically convex functions via Katuganpola fractional integrals, Researchgate Preprint, (2017), Available online from: https://www.researchgate.net/publication/319649734.
  • Prudnikov, A. P., Brychkov, Y. A. and Marichev, O. J., Integral and series, Elementary Functions, vol. 1, Nauka, Moscow, 1981.
  • Roberts, A. W. and Varberg, D. E., Convex functions, Academic Press, New York, 1973.
  • Şanlı, Z., Kunt, M. and Köroğlu, T., New Riemann-Liouville fractional Hermite Hadamard type inequalities for harmonically convex functions, ResearchGate Preprint, 2018, Doi: 10.13140/RG.2.2.14263.42400.
There are 20 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Review Articles
Authors

Zeynep Şanlı

Tuncay Köroğlu

Mehmet Kunt

Publication Date August 1, 2019
Submission Date April 6, 2018
Acceptance Date November 18, 2018
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Şanlı, Z., Köroğlu, T., & Kunt, M. (2019). Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1556-1575. https://doi.org/10.31801/cfsuasmas.413019
AMA Şanlı Z, Köroğlu T, Kunt M. Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1556-1575. doi:10.31801/cfsuasmas.413019
Chicago Şanlı, Zeynep, Tuncay Köroğlu, and Mehmet Kunt. “Improved Hermite Hadamard Type Inequalities for Harmonically Convex Functions via Katugampola Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1556-75. https://doi.org/10.31801/cfsuasmas.413019.
EndNote Şanlı Z, Köroğlu T, Kunt M (August 1, 2019) Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1556–1575.
IEEE Z. Şanlı, T. Köroğlu, and M. Kunt, “Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1556–1575, 2019, doi: 10.31801/cfsuasmas.413019.
ISNAD Şanlı, Zeynep et al. “Improved Hermite Hadamard Type Inequalities for Harmonically Convex Functions via Katugampola Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1556-1575. https://doi.org/10.31801/cfsuasmas.413019.
JAMA Şanlı Z, Köroğlu T, Kunt M. Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1556–1575.
MLA Şanlı, Zeynep et al. “Improved Hermite Hadamard Type Inequalities for Harmonically Convex Functions via Katugampola Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1556-75, doi:10.31801/cfsuasmas.413019.
Vancouver Şanlı Z, Köroğlu T, Kunt M. Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1556-75.

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