Liouville pdf

Keywords: Riemann-Liouville fractional derivative, positive sublinear operators, modulus of continuity, comonotonic operator, Choquet integral. Introduction In this paper among others we are motivated by the following results: First by P. Korovkin [9], , p. That is one derives the Korovkin conclu- sion in a quantitative way and with rates of convergence.

We continue this type as research here for positive sublinear operators over con- tinuous functions with existing left and right Riemann-Liouville fractional derivatives of order less than one.

We give applications. Main results We mention Definition 2. We need Lemma 2. We need Definition 2. We give Theorem 2. The theorem is proved. We make Remark 2. Then, by 2. All as in Theorem 2. Application 2. In [5], p. We present q Theorem 2. Choquet integral has become very important in statistical mechanics, potential theory, non-additive measure theory, and lately in economics.

For the definition and properties of Choquet integral R read [7], [8], [13]. We denote it by C. Next we talk about representations of positive sublinear operators by Choquet integrals: We need Definition 2. Theorem 2. Anastassiou We make Remark 2. That is here LN fulfills the positive homogenuity, mono- tonicity and subadditivity properties, see Definition 2.

By Theorem 2. We give applications. Main results We mention Definition 2. We need Lemma 2. We need Definition 2. We give Theorem 2. The theorem is proved. We make Remark 2. Then, by 2. All as in Theorem 2. Application 2. In [5], p. We present q Theorem 2. Choquet integral has become very important in statistical mechanics, potential theory, non-additive measure theory, and lately in economics.

For the definition and properties of Choquet integral R read [7], [8], [13]. We denote it by C. Next we talk about representations of positive sublinear operators by Choquet integrals: We need Definition 2.

Theorem 2. Anastassiou We make Remark 2. That is here LN fulfills the positive homogenuity, mono- tonicity and subadditivity properties, see Definition 2. By Theorem 2. In particular 2. We give q Theorem 2. Fourier Grenoble , 5 , Delhi, India, George A.