Research Article

On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions

Volume: 68 Number: 2 August 1, 2019
EN

On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions

Abstract

In this paper, we show that the power function fn(x) is hyperbolic
p-convex function. Furthermore, we establish some new integral inequalities
for higher powers of hyperbolic p-convex functions. Also, some applications
for special means are provided as well.

Keywords

References

  1. Mohamed, S. S. A., On certain properties for two classes of generalized convex functions, Abstract and Applied Analysis, (2016), Article ID 4652038, 7 pages.
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  3. Beckenbach, E. F. and Bing, R. H., On generalized convex functions, Transactions of the American Mathematical Society, vol. 58, (1945), 220-230.
  4. Peixoto, M. M., Generalized Convex Functions and Second Order Differential Inequalities, Bulletin of the American Mathematical Society, vol. 55, no. 6, (1949), 563-572.
  5. Toader, G. H., Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, University of Cluj-Napoca, (1984), 329-338.
  6. Hudzig, H., Maligranda, L., Some remarks ons-convex functions, Aequationes Mathematicae, vol. 48, no. 1, (1994), 100-111.
  7. Sarıkaya, M.Z., et al, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, vol. 57, no. 9, (2013), 2403-2407.
  8. Ion, D.A., Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of the University of Craiova-Mathematics and Computer Science Series, vol. 34, (2007), 82-87.

Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Publication Date

August 1, 2019

Submission Date

October 16, 2018

Acceptance Date

March 26, 2019

Published in Issue

Year 2019 Volume: 68 Number: 2

APA
Yehia, Z., Faried, N., & Ali, M. S. S. (2019). On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1841-1851. https://doi.org/10.31801/cfsuasmas.471397
AMA
1.Yehia Z, Faried N, Ali MSS. On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1841-1851. doi:10.31801/cfsuasmas.471397
Chicago
Yehia, Zeinab, Nashat Faried, and Mohamed S. S. Ali. 2019. “On Some New Inequalities of Hermite Hadamard Types for Hyperbolic P-Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2): 1841-51. https://doi.org/10.31801/cfsuasmas.471397.
EndNote
Yehia Z, Faried N, Ali MSS (August 1, 2019) On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1841–1851.
IEEE
[1]Z. Yehia, N. Faried, and M. S. S. Ali, “On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1841–1851, Aug. 2019, doi: 10.31801/cfsuasmas.471397.
ISNAD
Yehia, Zeinab - Faried, Nashat - Ali, Mohamed S. S. “On Some New Inequalities of Hermite Hadamard Types for Hyperbolic P-Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 1, 2019): 1841-1851. https://doi.org/10.31801/cfsuasmas.471397.
JAMA
1.Yehia Z, Faried N, Ali MSS. On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1841–1851.
MLA
Yehia, Zeinab, et al. “On Some New Inequalities of Hermite Hadamard Types for Hyperbolic P-Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, Aug. 2019, pp. 1841-5, doi:10.31801/cfsuasmas.471397.
Vancouver
1.Zeinab Yehia, Nashat Faried, Mohamed S. S. Ali. On some new inequalities of Hermite Hadamard types for hyperbolic p-convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019 Aug. 1;68(2):1841-5. doi:10.31801/cfsuasmas.471397

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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