Abstract:Abstract. We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over [a, b] ⊂ R, error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions. These inequalities are given for fuzzy Hölder and fuzzy differentiable functions and these facts are reflected in their right-hand sides.Mathematical subject classification: 26D07, 26D15, 26E50.
“…u − (α) is a bounded left continuous nondecreasing function over [0,1], with respect to any α; 2. u + (α) is a bounded left continuous nonincreasing function over [0,1], with respect to any α;…”
Section: Definition 21 ([7]mentioning
confidence: 99%
“…According to the importance of account deficits, more attention has been attracted and a lot of quality researches in this branch of mathematical analysis have been carried out, (see [3,10,21] and the references therein). Anastassiou [1,2] proved the fuzzy Ostrowski's inequalities. These inequalities have been applied for Euler's Beta mapping [22] and special means such as the arithmetic mean, the geometric mean, the harmonic mean and others.…”
In this paper, we mix both concepts of s-Godunova-Levin and m-convexity and introduce the (s,m)-Godunova-Levin functions. We introduce the fuzzy Hermite-Hadamard inequality for (s,m)-Godunova-Levin functions via fractional integral. Holder inequality is used for new bounds for fuzzy Hermite-Hadamard inequality. Then we accommodate this result with the previous works that have been done before. c 2016 All rights reserved.
“…u − (α) is a bounded left continuous nondecreasing function over [0,1], with respect to any α; 2. u + (α) is a bounded left continuous nonincreasing function over [0,1], with respect to any α;…”
Section: Definition 21 ([7]mentioning
confidence: 99%
“…According to the importance of account deficits, more attention has been attracted and a lot of quality researches in this branch of mathematical analysis have been carried out, (see [3,10,21] and the references therein). Anastassiou [1,2] proved the fuzzy Ostrowski's inequalities. These inequalities have been applied for Euler's Beta mapping [22] and special means such as the arithmetic mean, the geometric mean, the harmonic mean and others.…”
In this paper, we mix both concepts of s-Godunova-Levin and m-convexity and introduce the (s,m)-Godunova-Levin functions. We introduce the fuzzy Hermite-Hadamard inequality for (s,m)-Godunova-Levin functions via fractional integral. Holder inequality is used for new bounds for fuzzy Hermite-Hadamard inequality. Then we accommodate this result with the previous works that have been done before. c 2016 All rights reserved.
“…Since fuzziness is a natural reality different than randomness and determinism, Anastassiou (see [1], [2]) established fuzzy Ostrowski's inequalities. These inequalities have been applied to Euler's beta mapping (see [20]) and special means such as the arithmetic mean, geometric mean, harmonic mean, and others.…”
Section: Introductionmentioning
confidence: 99%
“…(1) u − (α) is a bounded left continuous nondecreasing function over [0,1], with respect to any α; (2) u + (α) is a bounded left continuous nonincreasing function over [0,1], with respect to any α;…”
Abstract. In the present paper, the notion of the generalized (s, m)-preinvex Godunova-Levin function of second kind is introduced and some uncertain fuzzy Ostrowski type inequalities for the generalized (s, m)-preinvex Godunova-Levin functions of second kind via classical integrals and Riemann-Liouville fractional integrals are established.
“…The first Ostrowski type inequality for fuzzy-valued functions was presented in [1] using the concept of Hukuhara differentiability [11]. More recently, Ostrowski type inequalities for interval-valued functions using generalized Hukuhara differentiability were presented in [9].…”
The present article presents new Ostrowski type inequalities for generalized Hukuhara differentible fuzzy-valued functions. As a consequence of this inequalities we present an error estimation to Riemann-type quadrature rule for fuzzyvalued functions.
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