TY - JOUR T1 - New General Inequalities For Exponential Type Convex Function AU - Yıldız, Çetin AU - Bakan, Emre AU - Dönmez, Hüseyin PY - 2023 DA - May JF - Turkish Journal of Science JO - TJOS PB - Ahmet Ocak AKDEMİR WT - DergiPark SN - 2587-0971 SP - 11 EP - 18 VL - 8 IS - 1 LA - en AB - In this paper, we introduce the concept of an exponential type convex function. We establish new integral inequalities of the Hermite-Hadamard type by using the Power-Mean and Hölder Inequalities. Additionally, we give the Riemann-Liouville fractional integrals definitions. We use these Riemann-Liouville fractional integrals to establish a new integral inequality for exponential type convex function. KW - Convex function KW - Exponential type convexity KW - Hermite-Hadamard inequalities CR - Alomari M.W., Dragomir S.S. and Kirmaci U.S., Generalizations of the Hermite-Hadamard type inequalities for functions whose derivatives are s-convex, Acta Commen. Uni. Tartu. Math., 17 (2), 2013. CR - Kadakal M., İşçan İ., Exponential Type Convexity and Some Related Inequalities. Journal of Inequalities and Application, CR - Özdemir M.E. and Kırmacı U. S. Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means, Appl. Math. Comp., 2003, 143: 269--274. CR - Hadamard J.: Êtude sur les propriêtês des fonctions entiêres en particullier d'une fonction considêrêê par Riemann. J. Math. Pures Appl. 58, 171-215 (1893) CR - Özdemir, M.E., Bayraktar, B., Butt. S.I. and Akdemir, A.O., Some New Hermite-Hadamard type inequalities Via Non-Conformable Fractional Integrals, Turkish J. Ineq., 5 (2) (2021), 48 --60. CR - Set, E., Akdemir, A.O., Karaoğlan, A., Abdeljawad, T. and Shatanawi, W., On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators, Axioms, 10(3)(2021), 223. CR - Özdemir, M. E., New Refinements of Hadamard Integral inequlaity via k-Fractional Integrals for p-Convex Function, Turkish Jour. Sci., 6 (1)(2021), 1-5. CR - Ekinci, A., Akdemir, A.O. and Özdemir, M.E., Integral Inequalities for Different Kinds of Convexity via Classical Inequalities, Turkish Jour. Sci, 5 (3)(2020), 305-313. CR - Ekinci, A., Özdemir, M.E. and Set, E., New Integral Inequalities of Ostrowski Type for Quasi-Convex Functions with Applications, Turkish Jour. Sci, 5 (3)(2020), 290-304. CR - Yıldız, Ç., Gürbüz, M. and Akdemir, A.O. The Hadamard Type Inequalities for M- Convex Functions. Konuralp Jour. Math., 1(1)(2013), 40-47. CR - Chu, Y.M., Khan, M.A., Khan, T.U. and Ali, T., Generalizations of Hermite-Hadamard type inequalities for MT-convex functions, J. Nonlinear Sci. Appl., 9(5)(2016), 4305-4316. CR - Khan, M.A., Chu, Y., Khan, T.U. and Khan, J., Some new inequalities of Hermite-Hadamard type for s-convex functions with applications, Open Mathematics, 15(1)(2017), 1414-1430. CR - R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276. CR - Özdemir, M.E., Dragomir, S.S. and Yıldız, Ç., The Hadamard Inequality For Convex Function Via Fractional Integrals, Acta Math. Sci., 33(5) (2013), 1293-1299. CR - İşcan, İ., New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl., 2019:304 (2019). UR - https://dergipark.org.tr/tr/pub/tjos/issue//1166878 L1 - https://dergipark.org.tr/tr/download/article-file/2615556 ER -