Continuous refinements of some Jensen-type inequalities via strong convexity with applications
نویسندگان
چکیده
Abstract In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications also derive Hermite–Hadamard, Hölder, Popoviciu inequalities. particular cases point out the corresponding results for sums integrals showing that our contain several well-known but these special cases.
منابع مشابه
(m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities
In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...
متن کاملOn some inequalities of Hermite-Hadamard type via m-convexity
Keywords: m-convex functions Hermite–Hadamard inequalities Hölder inequality Power-mean inequality a b s t r a c t In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m-convex.
متن کاملNew Jensen and Ostrowski Type Inequalities for General Lebesgue Integral with Applications
Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.
متن کاملSome extended Simpson-type inequalities and applications
In this paper, we shall establish some extended Simpson-type inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Simpson formula are also given.
متن کاملNew Inequalities of Hadamard-type via -Convexity
Some new Hermite-Hadamard’s inequalities for h-convex functions are proved, generalizing some results in [1, 3, 6] and unifying a number of known results. Some new applications for special means of real numbers are also deduced.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2022
ISSN: ['1025-5834', '1029-242X']
DOI: https://doi.org/10.1186/s13660-022-02801-4