TY - JOUR T1 - New Integral Inequalities for 𝒏-polynomial Exponential Type GA-Convex Functions TT - 𝒏-polynomial Üstel Tip GA-Konveks Fonksiyonlar için Yeni İntegral Eşitsizlikleri AU - Demirel, Ayşe Kübra PY - 2022 DA - April DO - 10.53433/yyufbed.1064363 JF - Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi JO - YYUFBED PB - Van Yüzüncü Yıl Üniversitesi WT - DergiPark SN - 1300-5413 SP - 181 EP - 193 VL - 27 IS - 1 LA - en AB - 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. KW - GA-convexity KW - n-polynomial convexity KW - Integral inequality N2 - Bu çalışmada, 𝑛-polinomal üstel tip GA-konveks fonksiyonlar adı verilen yeni bir konveks fonksiyon tipi tanıtılmıştır. Tanıtılan bu fonksiyonların bazı cebirsel özellikleri belirlenmiştir ve 𝑛-polinomal tip konveks fonksiyonlar için bazı yeni Hermite-Hadamard tipi integral eşitsizlikleri kanıtlanmıştır. CR - 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 CR - 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. CR - Budak, H., & Özçelik, K. (2020). On Hermite-Hadamard type inequalities for multiplicative fractional integrals. Miskolc Mathematical Notes, 21(1), 91-99. CR - 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. CR - 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). CR - 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. CR - El-Marouf, S. A. A. (2018). Generalization of Hilbert-Hardy integral inequalities. Kuwait Journal of Science, 45(1), 7-19. CR - 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. CR - 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. CR - İşcan, İ. (2020). Jensen–Mercer inequality for GA-convex functions and some related inequalities. Journal of Inequalities and Applications, 212(1). CR - Kadakal, M., & İşcan, İ. (2020). Exponential type convexity and some related inequalities. Moroccon Journal of Inequalities and Applications, 82. CR - 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. CR - Niculescu, P. C. (2000). Convexity according to the geometric mean. Mathematical Inequalities and Applications, 2(3), 155-167. CR - Niculescu, P. C. (2003). Convexity according to the mean. Mathematical Inequalities and Applications, 4(6), 571-579. CR - 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). CR - Noor, M. A., Noor, K. I., & Awan, M. U. (2020). Generalized fractional Hermite-Hadamard inequalities. Miskolc Mathematical Notes, 21(2), 1001-1011. CR - Toplu, T., Kadakal, M., & İşcan, İ. (2020). On n-polynomial convexity and some related inequalities. AIMS Mathematics, 5, 1304-1318. CR - 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. CR - 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. CR - 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. UR - https://doi.org/10.53433/yyufbed.1064363 L1 - https://dergipark.org.tr/tr/download/article-file/2218051 ER -