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Yıl 2021, Cilt: 70 Sayı: 1, 497 - 509, 30.06.2021

Selim Numan İmdat İşcan

https://doi.org/10.31801/cfsuasmas.745357

Öz

Kaynakça

  • Bombardelli, M., Varosanec, S., Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl., 58 (2009), 1869-1877, https://doi.org/10.1016/j.camwa.2009.07.073
  • Barani, A., Barani, S., Hermite-Hadamard type inequalities for functions when a power of the absolute value of the first derivative is P-convex, Bull. Aust. Math. Soc., 86 (1) (2012), 129-134, https://doi.org/10.1017/S0004972711003029
  • Bekar, K., Hermite-Hadamard Type Inequalities for Trigonometrically P-functions, Comptes rendus de l'Académie bulgare des Sciences, 72 (11) (2019), 1449-1457, doi:10.7546/CRABS.2019.11.01
  • Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95, https://doi.org/10.1016/S0893-9659(98)00086-X
  • Dragomir, S. S., Peµcari´c, J., Persson, L. E., Some inequalities of Hadamard type, Soochow Journal of Mathematics, 21 (3) (1995), 335-341.
  • Hadamard, J., Étude sur les propriétés des fonctions entières en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
  • İscan, İ., Set, E., Özdemir, M. E., Some new general integral inequalities for P-functions, Malaya J. Mat., 2 (4) (2014), 510-516.
  • İscan, İ., Olucak, V., Multiplicatively harmonically P-functions and some related inequalities, Sigma J. Eng. & Nat. Sci., 37 (2) (2019), 521-528.
  • Kadakal, M., İscan, İ., Kadakal, H., On new Simpson type inequalities for the p-quasi convex functions, Turkish J. Ineq., 2 (1) (2018), 30-37.
  • Kadakal, M., Karaca, H., İscan, İ., Hermite-Hadamard type inequalities for multiplicatively geometrically P-functions, Poincare Journal of Analysis & Application, 2 (1) (2018), 77-85.
  • Kadakal, M., İscan, İ., Exponential type convexity and some related inequalities, J. Inequal. Appl., 2020 (82) (2020), 1-9, https://doi.org/10.1186/s13660-020-02349-1
  • Latif, M. A., Du, T., Some generalized Hermite-Hadamard and Simpson type inequalities by using the p-convexity of differentiable mappings, Turkish J. Ineq., 2 (2) (2018), 23-36.
  • Set, E., Ardiç, M. A., Inequalities for log-convex and P-functions, Miskolc Math. Notes, 18 (2017), 1033-1041, doi: 10.18514/MMN.2017.1798
  • Varosanec, S., On h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311, https://doi.org/10.1016/j.jmaa.2006.02.086

On exponential type P-functions

Yıl 2021, Cilt: 70 Sayı: 1, 497 - 509, 30.06.2021

Selim Numan İmdat İşcan

https://doi.org/10.31801/cfsuasmas.745357

Öz

In this paper, we introduce and study the concept of exponential type P-function and establish Hermite-Hadamard's inequalities for this type of functions. In addition, we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P-function by using Hölder and power-mean integral inequalities. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula and for some inequalities related to special means of real numbers.

Anahtar Kelimeler

Exponential type convexity exponential type P-function Hermite-Hadamard inequality

Kaynakça

  • Bombardelli, M., Varosanec, S., Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl., 58 (2009), 1869-1877, https://doi.org/10.1016/j.camwa.2009.07.073
  • Barani, A., Barani, S., Hermite-Hadamard type inequalities for functions when a power of the absolute value of the first derivative is P-convex, Bull. Aust. Math. Soc., 86 (1) (2012), 129-134, https://doi.org/10.1017/S0004972711003029
  • Bekar, K., Hermite-Hadamard Type Inequalities for Trigonometrically P-functions, Comptes rendus de l'Académie bulgare des Sciences, 72 (11) (2019), 1449-1457, doi:10.7546/CRABS.2019.11.01
  • Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95, https://doi.org/10.1016/S0893-9659(98)00086-X
  • Dragomir, S. S., Peµcari´c, J., Persson, L. E., Some inequalities of Hadamard type, Soochow Journal of Mathematics, 21 (3) (1995), 335-341.
  • Hadamard, J., Étude sur les propriétés des fonctions entières en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171-215.
  • İscan, İ., Set, E., Özdemir, M. E., Some new general integral inequalities for P-functions, Malaya J. Mat., 2 (4) (2014), 510-516.
  • İscan, İ., Olucak, V., Multiplicatively harmonically P-functions and some related inequalities, Sigma J. Eng. & Nat. Sci., 37 (2) (2019), 521-528.
  • Kadakal, M., İscan, İ., Kadakal, H., On new Simpson type inequalities for the p-quasi convex functions, Turkish J. Ineq., 2 (1) (2018), 30-37.
  • Kadakal, M., Karaca, H., İscan, İ., Hermite-Hadamard type inequalities for multiplicatively geometrically P-functions, Poincare Journal of Analysis & Application, 2 (1) (2018), 77-85.
  • Kadakal, M., İscan, İ., Exponential type convexity and some related inequalities, J. Inequal. Appl., 2020 (82) (2020), 1-9, https://doi.org/10.1186/s13660-020-02349-1
  • Latif, M. A., Du, T., Some generalized Hermite-Hadamard and Simpson type inequalities by using the p-convexity of differentiable mappings, Turkish J. Ineq., 2 (2) (2018), 23-36.
  • Set, E., Ardiç, M. A., Inequalities for log-convex and P-functions, Miskolc Math. Notes, 18 (2017), 1033-1041, doi: 10.18514/MMN.2017.1798
  • Varosanec, S., On h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311, https://doi.org/10.1016/j.jmaa.2006.02.086
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Selim Numan 0000-0002-5483-6861

İmdat İşcan 0000-0001-6749-0591

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 30 Mayıs 2020
Kabul Tarihi 12 Şubat 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

APA Numan, S., & İşcan, İ. (2021). On exponential type P-functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 497-509. https://doi.org/10.31801/cfsuasmas.745357
AMA Numan S, İşcan İ. On exponential type P-functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2021;70(1):497-509. doi:10.31801/cfsuasmas.745357
Chicago Numan, Selim, ve İmdat İşcan. “On Exponential Type P-Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 497-509. https://doi.org/10.31801/cfsuasmas.745357.
EndNote Numan S, İşcan İ (01 Haziran 2021) On exponential type P-functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 497–509.
IEEE S. Numan ve İ. İşcan, “On exponential type P-functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 497–509, 2021, doi: 10.31801/cfsuasmas.745357.
ISNAD Numan, Selim - İşcan, İmdat. “On Exponential Type P-Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 2021), 497-509. https://doi.org/10.31801/cfsuasmas.745357.
JAMA Numan S, İşcan İ. On exponential type P-functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:497–509.
MLA Numan, Selim ve İmdat İşcan. “On Exponential Type P-Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 497-09, doi:10.31801/cfsuasmas.745357.
Vancouver Numan S, İşcan İ. On exponential type P-functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):497-509.

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

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