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EN
In the present paper, a new class of generalized beta (r, g)-preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving generalized beta (r, g)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized beta (r, g)-preinvex functions that are twice differentiable via k-fractional integrals are established. These general inequalities give us some new estimates for Hermite-Hadamard type k-fractional integral inequalities and also extend some results appeared in the literature; see [A. Kashuri and R. Liko, Ostrowski type fractional integral inequalities for generalized (s, m, φ)-preinvex functions, Aust. J. Math. Anal. Appl. 13 (2016), no. 1, Article ID 16]. At the end, some applications to special means are given.
2
EN
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
EN
In the paper, the authors obtain some Hermite–Hadamard type integral inequalities for extended s-convex functions on the co-ordinates in a rectangle.
EN
Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.
5
Content available remote On some new inequalities of Hermite-Hadamard-Fejer type involving convex functions
EN
In this paper, we establish some inequalities of Hermite-Hadamard-Fejér type for m-convex functions and s-convex functions.
6
Content available remote Hadamard's inequality for s-convex functions in the first sense and applications
EN
In this paper we extend the well-known Hadamard integral inequality which holds for convex functions to the case of s-convex functions in the first sense , which were considered by Orlicz and used in the theory of Orlicz spaces. Some applications for concrete mappings are also given.
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