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Hermite-Hadamard Type Inequalities for Multiplicatively P-Functions

Yıl 2020, , 486 - 491, 15.04.2020
https://doi.org/10.17714/gumusfenbil.664386

Öz

In
this study, we first establish some integral inequalities of Hermite-Hadamard
type in the setting of multiplicative calculus for multiplicatively
-functions.
Then, by using some properties of this kind of functions, we obtain new inequalities
involving multiplicative integrals for product and quotient of multiplicatively
-functions
and convex functions.

Destekleyen Kurum

Kırklareli Üniversitesi

Proje Numarası

KLUBAP-191

Kaynakça

  • Ali, M. A., Abbas, M., Zhang, Z., Sial, I. B. and Arif, R., 2019. On Integral Inequalities for Product and Quotient of Two Multiplicatively Convex Functions. Asian Research Journal of Mathematics, 12(3), 1-11.
  • Bashirov, A. E., Kurpınar, E. M. and Özyapıcı, A., 2008. Multiplicative Calculus and Applications. Journal of Mathematical Analysis and Applications, 337(1), 36-48.
  • Budak, H., Tunç, T. and Sarıkaya, M.Z., 2019. On Hermite-Hadamard Type Inequalities for F-Convex Function. Miskolc Mathematical Notes, 20(1), 169-191.
  • Dragomir, S. S. and Pearce, C. E. M., 1998. Quasi-Convex Functions and Hermite-Hadamard’s Inequality. Bulletin of the Australian Mathematical Society, 57, 377-385.
  • Dragomir, S. S. and Pearce, C. E. M., 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 357 p.
  • Dragomir, S. S., Pecaric, J. and Persson, L. E., 1995. Some Inequalities of Hadamard Type. Soochow Journal of Mathematics, 21(3), 335-341.
  • Kadakal, H., 2018. Multiplicatively P-Functions and Some New Inequalities. New Trends in Mathematical Sciences, 6(4), 111-118.
  • Kadakal, H., 2019. Some Integral Inequalities for Multiplicatively Geometrically P-Functions. An International Journal of Optimization and Control: Theories & Applications, 9(2), 216-222.
  • Kadakal, M., 2019. Hermite-Hadamard and Simpson Type Inequalities for Multiplicatively Harmonically P-Functions. Sigma Journal of Engineering and Natural Sciences, 37(4), 1311-1320.
  • Maden, S., Demirel, A.K., Turhan, S. and İşcan, İ., 2018. Some Integral Inequalities for the New Convex Functions. Sigma Journal of Engineering and Natural Sciences, 9(3), 319-326.
  • Özcan, S., 2019. Some Integral Inequalities for Harmonically (α,s)-Convex Functions. Journal of Function Spaces, Vol. 2019, Article ID 2394021, 8 pages.
  • Özcan, S. and İşcan, İ., 2019. Some New Hermite-Hadamard Type Inequalities for s-Convex Functions and Their Applications. Journal of İnequalities and Applications, Article number: 2019:201, 11 pages.
  • Özdemir, M.E., Önalan, H.K. and Ardıç, M.A., 2015. Hermite-Hadamard Type Inequalities for (h-(α,m))-Convex Functions. Journal of Concrete & Applicable Mathematics, 13, 96-107.
  • Pečarić, J. E., Proschan, F. and Tong, Y. L., 1992. Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 467 p.
  • Sarıkaya, M.Z., Akkurt, A., Budak, H., Yıldırım, M.E. and Yıldırım, H., 2019. Hermite-Hadamard's Inequalities for Conformable Fractional Integrals. An International Journal of Optimization and Control: Theories & Applications, 9(1), 49-59.
  • Set, E., İşcan, İ., Sarıkaya, M. Z. and Özdemir, M. E., 2015. On New Inequalities of Hermite-Hadamard-Fejer Type for Convex Functions via Fractional Integrals. Applied Mathematics and Computation, 259, 875-881.

Çarpımsal P-Fonksiyonlar İçin Hermite-Hadamard Tipli Eşitsizlikler

Yıl 2020, , 486 - 491, 15.04.2020
https://doi.org/10.17714/gumusfenbil.664386

Öz

Bu çalışmada, öncelikle, çarpımsal -fonksiyonlar için çarpımsal kalkülüs ortamında Hermite-Hadamard tipi
bazı integral eşitsizlikleri oluşturulmuştur. Daha sonra, bu tür fonksiyonların
bazı özellikleri kullanılarak, çarpımsal P-fonksiyonlar ile konveks
fonksiyonların çarpım ve bölümleri için çarpımsal integralleri içeren yeni
eşitsizlikler elde edilmiştir.

Proje Numarası

KLUBAP-191

Kaynakça

  • Ali, M. A., Abbas, M., Zhang, Z., Sial, I. B. and Arif, R., 2019. On Integral Inequalities for Product and Quotient of Two Multiplicatively Convex Functions. Asian Research Journal of Mathematics, 12(3), 1-11.
  • Bashirov, A. E., Kurpınar, E. M. and Özyapıcı, A., 2008. Multiplicative Calculus and Applications. Journal of Mathematical Analysis and Applications, 337(1), 36-48.
  • Budak, H., Tunç, T. and Sarıkaya, M.Z., 2019. On Hermite-Hadamard Type Inequalities for F-Convex Function. Miskolc Mathematical Notes, 20(1), 169-191.
  • Dragomir, S. S. and Pearce, C. E. M., 1998. Quasi-Convex Functions and Hermite-Hadamard’s Inequality. Bulletin of the Australian Mathematical Society, 57, 377-385.
  • Dragomir, S. S. and Pearce, C. E. M., 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 357 p.
  • Dragomir, S. S., Pecaric, J. and Persson, L. E., 1995. Some Inequalities of Hadamard Type. Soochow Journal of Mathematics, 21(3), 335-341.
  • Kadakal, H., 2018. Multiplicatively P-Functions and Some New Inequalities. New Trends in Mathematical Sciences, 6(4), 111-118.
  • Kadakal, H., 2019. Some Integral Inequalities for Multiplicatively Geometrically P-Functions. An International Journal of Optimization and Control: Theories & Applications, 9(2), 216-222.
  • Kadakal, M., 2019. Hermite-Hadamard and Simpson Type Inequalities for Multiplicatively Harmonically P-Functions. Sigma Journal of Engineering and Natural Sciences, 37(4), 1311-1320.
  • Maden, S., Demirel, A.K., Turhan, S. and İşcan, İ., 2018. Some Integral Inequalities for the New Convex Functions. Sigma Journal of Engineering and Natural Sciences, 9(3), 319-326.
  • Özcan, S., 2019. Some Integral Inequalities for Harmonically (α,s)-Convex Functions. Journal of Function Spaces, Vol. 2019, Article ID 2394021, 8 pages.
  • Özcan, S. and İşcan, İ., 2019. Some New Hermite-Hadamard Type Inequalities for s-Convex Functions and Their Applications. Journal of İnequalities and Applications, Article number: 2019:201, 11 pages.
  • Özdemir, M.E., Önalan, H.K. and Ardıç, M.A., 2015. Hermite-Hadamard Type Inequalities for (h-(α,m))-Convex Functions. Journal of Concrete & Applicable Mathematics, 13, 96-107.
  • Pečarić, J. E., Proschan, F. and Tong, Y. L., 1992. Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 467 p.
  • Sarıkaya, M.Z., Akkurt, A., Budak, H., Yıldırım, M.E. and Yıldırım, H., 2019. Hermite-Hadamard's Inequalities for Conformable Fractional Integrals. An International Journal of Optimization and Control: Theories & Applications, 9(1), 49-59.
  • Set, E., İşcan, İ., Sarıkaya, M. Z. and Özdemir, M. E., 2015. On New Inequalities of Hermite-Hadamard-Fejer Type for Convex Functions via Fractional Integrals. Applied Mathematics and Computation, 259, 875-881.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Serap Özcan 0000-0001-6496-5088

Proje Numarası KLUBAP-191
Yayımlanma Tarihi 15 Nisan 2020
Gönderilme Tarihi 24 Aralık 2019
Kabul Tarihi 6 Mart 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Özcan, S. (2020). Çarpımsal P-Fonksiyonlar İçin Hermite-Hadamard Tipli Eşitsizlikler. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(2), 486-491. https://doi.org/10.17714/gumusfenbil.664386