Fuzzy Ostrowski type inequalities

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.

Uncertain Hermite-Hadamard inequality for functions with (s,m)-Godunova-Levin derivatives via fractional integral

“…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;…”

“…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.…”

Uncertain fuzzy Ostrowski type inequalities for the generalized (s,m)-preinvex Godunova-Levin functions of second kind

“…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.…”

“…(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;…”

A generalization of Ostrowski type inequalities for fuzzy-valued functions

“…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].…”