On Ostrowski-type inequalities for functions whose derivatives are m-convex and (alph, m)-convex functions with applications

Abstract

Abstract. In this paper we establish variant inequalities of Ostrowski's type for functions whose derivatives in absolute value are m-convex and (α, m)-convex. Applications to some special means are obtained.

Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables

“…468]) as stated in the following theorem. In recent years, various generalizations of the Ostrowski inequality including continuous and discrete versions have been established (for example, see [3][4][5][6][7][8][9][10][11][12][13][14] and the references therein). On the other hand, Hilger [15] initiated the theory of time scales as a theory capable of treating continuous and discrete analysis in a consistent way, based on which some authors have studied the Ostrowski type inequalities on time scales (see [16][17][18][19][20][21][22][23][24]).…”

Some new fractional integral inequalities for s-convex functions

“…The constant k = 1 s+1 is the best possible in the second inequality in (1.3). For other recent result concerning s-convex functions, see [2,5,8,16,17]. We will now give definitions of the right-hand side and left-hand side Riemann-Liouville fractional integrals which are used throughout this paper.…”

“…The inequality (1.1) can be expressed in the following form: . In recent years, many researchers have studied inequalities (1.1) and (1.2), for instance see [1,2,6,7,9,10,12,13,[15][16][17].…”

Ostrowski type inequalities for $p$-convex functions

“…In the literature, the inequality (1) is known as Ostrowski inequality (see [18]), which gives an upper bound for the approximation of the integral average 1 b−a b a f (t)dt by the value f (x) at point x ∈ [a, b]. In [3,5,6,9,10,11], the reader can find generalizations, improvements and extensions for the inequality (1). For p ∈ R the power mean M p (a, b) of order p of two positive numbers a and b is defined by Let M be the family of all mean values of two numbers in R + = (0, ∞) .…”