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

Yıl 2019, Cilt: 68 Sayı: 2, 1841 - 1851, 01.08.2019
https://doi.org/10.31801/cfsuasmas.471397

Öz

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.

Kaynakça

  • Mohamed, S. S. A., On certain properties for two classes of generalized convex functions, Abstract and Applied Analysis, (2016), Article ID 4652038, 7 pages.
  • Beckenbach, E. F., Generalized convex functions, Bulletin of the American Mathematical Society, vol. 43, no. 6, (1937), 363-371.
  • Beckenbach, E. F. and Bing, R. H., On generalized convex functions, Transactions of the American Mathematical Society, vol. 58, (1945), 220-230.
  • Peixoto, M. M., Generalized Convex Functions and Second Order Differential Inequalities, Bulletin of the American Mathematical Society, vol. 55, no. 6, (1949), 563-572.
  • Toader, G. H., Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, University of Cluj-Napoca, (1984), 329-338.
  • Hudzig, H., Maligranda, L., Some remarks ons-convex functions, Aequationes Mathematicae, vol. 48, no. 1, (1994), 100-111.
  • 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.
  • 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.
  • Dragomir, S.S., On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang Journal of Mathematics, vol. 33, no. 1, (2002), 45-56.
  • Dragomir, S. S., Some inequalities of Hermite-Hadamard type for hyperbolic p-convex functions, RGMIA Res. Rep. Coll, 2018.
  • Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and products, Academic Press, New York-London, 1983.
Yıl 2019, Cilt: 68 Sayı: 2, 1841 - 1851, 01.08.2019
https://doi.org/10.31801/cfsuasmas.471397

Öz

Kaynakça

  • Mohamed, S. S. A., On certain properties for two classes of generalized convex functions, Abstract and Applied Analysis, (2016), Article ID 4652038, 7 pages.
  • Beckenbach, E. F., Generalized convex functions, Bulletin of the American Mathematical Society, vol. 43, no. 6, (1937), 363-371.
  • Beckenbach, E. F. and Bing, R. H., On generalized convex functions, Transactions of the American Mathematical Society, vol. 58, (1945), 220-230.
  • Peixoto, M. M., Generalized Convex Functions and Second Order Differential Inequalities, Bulletin of the American Mathematical Society, vol. 55, no. 6, (1949), 563-572.
  • Toader, G. H., Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, University of Cluj-Napoca, (1984), 329-338.
  • Hudzig, H., Maligranda, L., Some remarks ons-convex functions, Aequationes Mathematicae, vol. 48, no. 1, (1994), 100-111.
  • 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.
  • 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.
  • Dragomir, S.S., On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang Journal of Mathematics, vol. 33, no. 1, (2002), 45-56.
  • Dragomir, S. S., Some inequalities of Hermite-Hadamard type for hyperbolic p-convex functions, RGMIA Res. Rep. Coll, 2018.
  • Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and products, Academic Press, New York-London, 1983.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Makaleler
Yazarlar

Zeinab Yehia 0000-0002-0263-9049

Nashat Faried Bu kişi benim 0000-0002-9593-9699

Mohamed S. S. Ali Bu kişi benim 0000-0002-2219-6038

Yayımlanma Tarihi 1 Ağustos 2019
Gönderilme Tarihi 16 Ekim 2018
Kabul Tarihi 26 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 2

Kaynak Göster

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 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. Ağustos 2019;68(2):1841-1851. doi:10.31801/cfsuasmas.471397
Chicago Yehia, Zeinab, Nashat Faried, ve Mohamed S. S. Ali. “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, sy. 2 (Ağustos 2019): 1841-51. https://doi.org/10.31801/cfsuasmas.471397.
EndNote Yehia Z, Faried N, Ali MSS (01 Ağustos 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 Z. Yehia, N. Faried, ve 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., c. 68, sy. 2, ss. 1841–1851, 2019, doi: 10.31801/cfsuasmas.471397.
ISNAD Yehia, Zeinab vd. “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 (Ağustos 2019), 1841-1851. https://doi.org/10.31801/cfsuasmas.471397.
JAMA 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 vd. “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, c. 68, sy. 2, 2019, ss. 1841-5, doi:10.31801/cfsuasmas.471397.
Vancouver 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):1841-5.

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

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