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In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. On the other hand, a general inequality is studied, which gives Hermite-Hadamard, Bullen and Simpson inequalities. Also, they gave some applications for special means for arbitrary positive numbers. [ABSTRACT FROM AUTHOR]

In this paper, is defined the operator Dλ,ν,nα,β : A → A, given by Dλ,ν,nα,β f(z) = (1 - α - β)RνDnf(z) + αRνΩλzf(z) + βDnΩλzf(z), for z ∈ U, where Rν is the Ruscheweyh derivative, Dn is the Sălăgean operator, Ωλz is a fractional differintegral operator introduced by S. Owa and H. M. Srivastava, A = {f ∈ H(U) : f(z) = z + a2z² + a3z³ + ..., z ∈ U}, α, β ≥ 0, ν > -1, n ∈ N0 = {0, 1, 2, 3, ...}, -∞ < λ < 2. A certain subclass of analytic functions in the open unit disk, Rλ,ν,nα,β (δ), where 0 ≤ δ ≤ 1, is introduced using the new operator. Are obtained some properties of the class Rλ,ν,nα,β (δ) and some differential subordinations using the operator Dλ,ν,nα,β. [ABSTRACT FROM AUTHOR]

Let 풜 be the class of normalized functions which are analytic in the open unit disc. Jakson q-derivative represented by convolution operator D q f (z) = 1 z { f (z) ★ z (1 - q z) (1 z) } , f ∈ 풜 , q ∈ (0 , 1) is used to introduce a unified class Mq(α, β, γ), α ≥ 0, β, γ ∈ [0, 1) and its various mapping properties are studied. For q → 1−1, β = γ = 0 and α = 1, this class reduces to the class K of close-to-convex univalent functions. A number of interesting results such as q-Bernardi integral operator and inclusion relations are included as part of this study. Applications are also pointed out as consequences of the main results. [ABSTRACT FROM AUTHOR]

To investigate approximation properties of integrable functions, Durrmeyer and Kantorovich modification of approximation operators are main tool. To combine these modification for Baskakov operators, we recently introduced a generalization of Baskakov operators in [6]. In this paper, we investigate pointwise convergence of derivatives of these operators by the means of Voronovskaya type asymptotic formula. This formula is presented in quantitative form in terms of a modulus of smoothness, which allows us describe the rate of pointwise convergence and the upper bound for the error of approximation simultaneously. [ABSTRACT FROM AUTHOR]

In this paper we consider a mean-value theorem. For this one we study the properties of the intermediate point and formulate some important results related to its derivatives. [ABSTRACT FROM AUTHOR]

In this paper we consider two continuous functions f, g : [a, b] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order differentiable at the point x = a and we calculate its derivative. [ABSTRACT FROM AUTHOR]

In this paper, four new estimates E2k-1,0, E2k-1,1, E2k-1,2 and E2k-1, M of a function f with its third derivative f(3) belonging to Lipα[0, 1] 0 < α ≤ 1, are obtained by Legendre wavelet method. These estimators are new, sharper and best possible in Wavelet Analysis. [ABSTRACT FROM AUTHOR]

If the functions f, g : [a, b] → R satisfy the conditions: (a) f and g are continuous on [a, b], (b) the function f is decreasing on [a, b], (c) f (x) ≤ 0, for all x ∈ [a, b], then there exists a point c ∈ [a, b] such that ... In this paper, we study the approaching of the point c towards a, when b approaches a. [ABSTRACT FROM AUTHOR]

In this current study, we introduce and investigate a new subclass of holormorphic and bi-univalent functions En, (R) in the unit disk X associated with q-derivative operator. The coefficient estimates |b2| and |b31 on the new subclass are obtained and important results are indicated. [ABSTRACT FROM AUTHOR]