[PDF] Top 20 Trapezoidal Type Inequalities for n-Time Differentiable Functions

... Note that for n = 1 and the infinite norm, Theorem 2 reduces to Theorem 1. In the next section we develop an integral equality that will permit us to obtain bounds for the error estimate in a generalised trapezoid ... See full document

... Theorem 2.1. For ∀𝑛 ∈ ℕ ; let 𝑓: 𝐼 ⊂ [0, ∞) → ℝ be 𝑛 -times differentiable function on 𝐼 ° and 𝑎, 𝑏 ∈ 𝐼 ° with 𝑎 < 𝑏 . If �𝑓 (𝑛) � 𝑞 ∈ 𝐿[𝑎, 𝑏] and �𝑓 (𝑛) � 𝑞 for 𝑞 > 1 is 𝑠 -convex function in the second ... See full document

... Remark 7. It is instructive to note that the relative location of α ( · ) and β ( · ) is the same in Corollary 4 and is determined through the parameter γ as defined in (2.13). Theorem 2 is much more general. From (2.13) ... See full document

... Abstract. The paper consists of some extensions in Hardy and Copson type inequalities on time scales. The main results are proved by using induction principle, Rules to find derivatives for ... See full document

... ˙Iscan, Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions, Journal of Mathematics, 2014 (2014), Article ID 346305.. [8] ˙I.[r] ... See full document

... these inequalities much work has been done, and many papers which deal with new proofs, various generalizations and extensions have appeared in the ...Gronwall-Bellman type inequalities are important ... See full document

... Jensen’s type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces, Filomat 23 (2009), ...Grüss’ type inequalities for functions of ... See full document

... the trapezoidal version and E (f, d) denotes the associated approximation ...a differentiable mapping on I° such that f’ Î L [a, b], where a, b Î I with a <b and | f | p−1 p is convex on [a, b], where p ... See full document

... (22) Proof. The proof is immediate from Corollary 4 with f x y ( ) , = x y m n , x y , ∈  , m n , ∈  , m ≥ 2 , n ≥ 2 . Proposition 2. Suppose a , b , c , d ∈  , a b < , c d < , 0 ∉ [ ] a b , ... See full document

... WANG, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl.. WANG, A new inequality of Ostrowski’s ty[r] ... See full document

... Rules have been developed that do not necessarily require the second derivative to be well behaved or indeed, exist, thus allowing the treatment of a much larger class of functions. Rules have been developed by ... See full document

... new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are s-convex ...several inequalities of Hermite-Hadamard type can be derived in ... See full document

... Pachpatte, New inequalities of Ostrowski and Trapezoid type for n-time differentiable functions, Bull.. Tong, Convex Function, Partial Ordering and Statistical Applications, Academic Pre[r] ... See full document

... In recent decades, plenty of inequalities of Hermite-Hadamard type for various kinds of convex functions have been established. Some of them may be reformulated as follows. Theorem . ([, Theorem ... See full document

... Abstract In the paper, by creating an integral identity involving an n-times differentiable function, the authors establish some new Hermite-Hadamard type inequalities for preinvex functi[r] ... See full document

... such inequalities have been ...Hermite-Hadamard type inequalities through various classes of convex functions, (see [11]) and the references cited therein, also (see [10]) and the references ... See full document

... WANG, Applications of Ostrowski's inequality to the estimation of error bounds for some special means and some numerical quadrature rules, Appl.. PECARIC and A.M[r] ... See full document

... Hermite-Hadamard type inequalities for con- formable fractional integrals, present some new inequalities for the arithmetic, logarith- mic and generalized logarithmic means of two positive real ... See full document

... In [], Alomari et al. established Hermite-Hadamard-type inequalities for quasi-convex functions which give refinements of those given above in Theorem  and Theorem . Theorem  [] Let f : I ⊆ [, ... See full document

... for functions defined on a rectangle from the plane is ...integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the ... See full document