TY  - JOUR
T1  - Refinements Jensen's Inequality and Some Their Applications
AU  - Sarikaya, Mehmet Zeki
PY  - 2024
DA  - October
Y2  - 2024
JF  - Konuralp Journal of Mathematics
JO  - Konuralp J. Math.
PB  - Mehmet Zeki SARIKAYA
WT  - DergiPark
SN  - 2147-625X
SP  - 112
EP  - 119
VL  - 12
IS  - 2
LA  - en
AB  - This paper aims to present a new refinement of the Jensen inequality specifically for convex functions. Building on this refinement, the paper derives various related inequalities, with a particular focus on Bullen's inequality and Ostrowski's inequality. Furthermore, it explores practical applications of these derived inequalities in the context of mean inequalities, providing a deeper understanding and broader utility of these mathematical concepts.
KW  - Convex function
KW  - Bullen inequality
KW  - Jensen inequality
KW  - Ostrowski inequality and Special means
CR  - [1] S. Abramovich, G. Jameson and G. Sinnamon, Refining Jensen’s inequality. Bulletin math´ematique de la Societe des Sciences Mathematiques de
Roumanie, 2004, 3-14.
CR  - [2] M. Çakmak, The differentiable h-convex functions involving the Bullen inequality, Acta Univ. Apulensis 2021, 65, 29–36.
CR  - [3] M. Çakmak, On some Bullen-type inequalities via conformable fractional integrals, J. Sci. Perspect. 3(4), 285–298, 2019.
CR  - [4] S. S. Dragomir, Ostrowski type inequalities for functions whose derivatives are h-convex in absolute value, Tbilisi Mathematical Journal 7(1) (2014), pp.
1–17.
CR  - [5] S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University,
2000.
CR  - [6] T. Du, C. Luo and Z. Cao, On the Bullen-type inequalities via generalized fractional integrals and their applications, Fractals, 29(07), 2150188, 2021.
CR  - [7] S. Erden and M. Z. Sarikaya, Generalized Bullen type inequalities for local fractional integrals and its applications, Palestine Journal of Mathematics,
9(2), 2020.
CR  - [8] A. Fahad, S. I. Butt, B. Bayraktar, M. Anwar and Y. Wang, Some new Bullen-type inequalities obtained via fractional integral operators. Axioms, 12(7),
691, 2023.
CR  - [9] F. Hezenci, H. Budak and H. Kara, A study on conformable fractional version of Bullen-type inequalities. Turkish Journal of Mathematics, 47(4),
1306-1317, 2023.
CR  - [10] S. Hussain and S. Mehboob, On some generalized fractional integral Bullen type inequalities with applications, J. Fract. Calc. Nonlinear Syst. 2021, 2,
93–112.
CR  - [11] L Horvath, A refinement of the integral form of Jensen’s inequality. Journal of Inequalities and Applications, 2012, 1-19, 2012.
CR  - [12] I. Işcan, T. Toplu and F. Yetgin, Some new inequalities on generalization of Hermite–Hadamard and Bullen type inequalities, applications to trapezoidal
and midpoint formula, Kragujev. J. Math. 45(4), 647–657, 2021.
CR  - [13] M.A Khan, J. Khan and J. Pecaric, Generalization of Jensen’s and Jensen-Steffensen’s inequalities by generalized majorization theorem. J. Math.
Inequal, 11(4), 2017, 1049-1074.
CR  - [14] C. Niculescu and L.E. Persson, Convex functions and their applications (Vol. 23). New York: Springer, 2006.
CR  - [15] D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Mathematics and its Applications (East European Series),
61. Kluwer Academic Publishers Group, Dordrecht, 1993.
CR  - [16] A. Ostrowski, Uber die Absolutabweichung einer differenzierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv., 10(1) (1937),
226227.
CR  - [17] H. Öğülmüş¸ and M. Z. Sarikaya, Some Hermite–Hadamard type inequalities for h-convex functions and their applications. Iranian Journal of Science
and Technology, Transactions A: Science, 44, 813-819, (2020).
UR  - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//1557009
L1  - https://dergipark.org.tr/en/download/article-file/4245171
ER  -