Dergiler / Konuralp Journal of Mathematics / 2017 / Cilt: 5 Sayı: 2

A NEW DEFINITION AND PROPERTIES OF QUANTUM INTEGRAL WHICH CALLS $\overline{q}$-INTEGRAL

Sayfa
146–159
Yayın Tarihi
2017-10-15
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finaly, we establish some new $\overline{q}$-Hermite-Hadamard type inequalities for convex functions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we present a new definition of $q$-integral by using trapezoid pieces and we name second sense $q$-integral which is showed $ \overline{q}$-integral and we give some results and properties of $\overline{ q}$-integral.
📊
Temel Bulgular & Veri:In this paper, we present a new definition of $q$-integral by using trapezoid pieces and we name second sense $q$-integral which is showed $ \overline{q}$-integral and we give some results and properties of $\overline{ q}$-integral.
💡
Sonuç & Katkı:Finaly, we establish some new $\overline{q}$-Hermite-Hadamard type inequalities for convex functions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hermite-Hadamard's inequalities · convex functions · q-integrals

Abstract

In this paper, we present a new definition of $q$-integral by using trapezoid pieces and we name second sense $q$-integral which is showed $ \overline{q}$-integral and we give some results and properties of $\overline{ q}$-integral. Finaly, we establish some new $\overline{q}$-Hermite-Hadamard type inequalities for convex functions.

🔖

Bu Makaleye Atıf Yap

ALP, N., SARIKAYA, M. Z. (2017). A NEW DEFINITION AND PROPERTIES OF QUANTUM INTEGRAL WHICH CALLS $\overline{q}$-INTEGRAL. Konuralp Journal of Mathematics, Cilt: 5 Sayı: 2, 146–159. https://ajindex.com/articles/908896

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (12)

  1. N. Alp, M. Z. Sarikaya, M. Kunt and ·I. ·I¸scan, q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, Journal of King Saud University - Science, 2016, dx.doi.org/10.1016/j.jksus.2016.09.007
  2. S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math. 2009., 10: Article ID 86
  3. Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 2010, 9: 493–497
  4. T. Ernst, A method for q-calculus. J. Nonlinear Math. Phys. 10 (4), 487–525 (2003)
  5. H. Gauchman, Integral inequalities in q-calculus, Comput. Math. Appl. 2004, 47: 281–300. 10.1016/S0898-1221(04)90025-9
  6. J. Hadamard, Etude sur les propri´ et´ es des fonctions enti´ eres et en particulier dune fonc- tion consider´ ee par Riemann, J. Math. Pures Appl. 58 (1893) 171–215
  7. V. Kac and P. Cheung, Quantum Calculus, Springer, New York, 2002
  8. M. A. Noor, K. I. Noor and M. U. Awan, Some Quantum estimates for Hermite–Hadamard inequalities, Appl. Math. Comput. 251, 675–679 (2015)
  9. M. A. Noor, K. I. Noor and M. U. Awan, Quantum Ostrowski inequalities for q-di¤ erentiable convex functions, J. Math. Inequlities, (2016)
  10. H. Ogunmez and U.M. Ozkan, Fractional quantum integral inequalities, J. Inequal. Appl. 2011., 2011: Article ID 787939 [11] W. Sudsutad and S. K. Ntouyas, J. Tariboon, Quantum integral inequalities for convex functions, Jour. Math Ineq. Volume 9, Number 3 (2015), 781–793
  11. J. Tariboon, S. K. Ntouyas, Quantum calculus on nite intervals and applications to impul- sive di¤ erence equations, Adv. Di¤er. Equ. 2013, 2013:282
  12. J. Tariboon and S. K. Ntouyas, Quantum integral inequalities on nite intervals, J. Inequal. Appl. 2014, 2014:121.