Ayşe Kübra DEMİREL

?-polynomial Üstel Tip GA-Konveks Fonksiyonlar için Yeni İntegral Eşitsizlikleri

Bu çalışmada, ?-polinomal üstel tip GA-konveks fonksiyonlar adı verilen yeni bir konveks fonksiyon tipi tanıtılmıştır. Tanıtılan bu fonksiyonların bazı cebirsel özellikleri belirlenmiştir ve ?-polinomal tip konveks fonksiyonlar için bazı yeni Hermite-Hadamard tipi integral eşitsizlikleri kanıtlanmıştır.

Anahtar Kelimeler:

GA-konvekslik, n-polinomal konvekslik, İntegral eşitsizliği

New Integral Inequalities for ?-polynomial Exponential Type GA-Convex Functions

In this paper, a new type of convex function called n-polynomial exponential type GA-convex functions is introduced. Some algebraic properties of these introduced functions are determined and the new Hermite-Hadamard type inequalities are proved for n-polynomial exponential type convex functions.

Keywords:

GA-convexity, n-polynomial convexity, Integral inequality,

PDF

___

Awan, M. U., Akhtar, N., Iftikhar, S., Noor, M. A., & Chu, Y. M. (2020a). New Hermite-Hadamard type inequalities for n-polynomial harmonically convex functions. In Journal of Inequalities and Applications, 125. doi: 10.1186/s13660-020-02393-x
Awan, M. U., Noor, M. A., Safdar, F., Islam, A., Mihai, M. V., & Noor, K. I. (2020b). Hermite-Hadamard type inequalities with applications. Miskolc Mathematical Notes, 21(2), 593-614.
Budak, H., & Özçelik, K. (2020). On Hermite-Hadamard type inequalities for multiplicative fractional integrals. Miskolc Mathematical Notes, 21(1), 91-99.
Butt, S. I., Kashuri, A., Tariq, M., Nasir, J., Aslam, A., & Gao, W. (2020a). Hermite-Hadamard type inequalities n–polynomial exponential type convexity and their applications. Advances in Difference Equations, 508.
Butt, S. I., Kashuri, A., Tariq, M., Nasir, J., Aslam, A., & Gao, W. (2020b). n–polynomial exponential type p–convex function with some related inequalities and their applications. Heliyon, 6(11).
Chen, S. B., Rashid, S., Noor, M. A., Hammouch, Z., & Chu, Y. M. (2020). New fractional approaches for n-polynomial p-convexity with applications in special function theory. Advances in Difference Equations, 543.
El-Marouf, S. A. A. (2018). Generalization of Hilbert-Hardy integral inequalities. Kuwait Journal of Science, 45(1), 7-19.
Gao, W., Kashuri, A., Butt, S. I., Tariq, M., Aslam, A., & Nadeem, M. (2020). New inequalities via n–polynomial harmonically exponential type p–convex functions. AIMS Mathematics, 5(6), 6856-6873.
İşcan, İ., & Turhan, S. (2016). Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via fractional integral. Moroccon Journal of Pure and Applied Analysis, 2(1), 34-46.
İşcan, İ. (2020). Jensen–Mercer inequality for GA-convex functions and some related inequalities. Journal of Inequalities and Applications, 212(1).
Kadakal, M., & İşcan, İ. (2020). Exponential type convexity and some related inequalities. Moroccon Journal of Inequalities and Applications, 82.
Khurshid, Y., Khan, M. A., & Chu, Y. M. (2020). Conformable fractional integral inequalities for GG and GA-convex functions. AIMS Mathematics, 5(5), 5012-5030.
Niculescu, P. C. (2000). Convexity according to the geometric mean. Mathematical Inequalities and Applications, 2(3), 155-167.
Niculescu, P. C. (2003). Convexity according to the mean. Mathematical Inequalities and Applications, 4(6), 571-579.
Noor, M. A., & Noor, K. I. (2020). New classes of exponentially general convex functions. University Politehnica of Bucharest Scientific Bulletin Series A: Applied Mathmematics and Physics, 82(3).
Noor, M. A., Noor, K. I., & Awan, M. U. (2020). Generalized fractional Hermite-Hadamard inequalities. Miskolc Mathematical Notes, 21(2), 1001-1011.
Toplu, T., Kadakal, M., & İşcan, İ. (2020). On n-polynomial convexity and some related inequalities. AIMS Mathematics, 5, 1304-1318.
Rashid, S., Noor, M. A., Noor, K. I., & Akdemir, A. O. (2019). Some new generalizations for exponentially s-convex functions and inequalities via fractional operators. Fractal and Fractional, 3(24), 2-16.
Rashid, S., Noor, M. A., Noor, K. I., & Safdar, F. (2020). New Hermite-Hadamard type inequalities for exponentially GA and GG-convex functions. Punjab University Journal of Mathematics, 52(2), 15-28.
Zhang, T. Y., Ji, A. P., & Qi, F. (2013). Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means. Le Matematiche, 8, 229-239.