Reverse convolution inequalities and applications to inverse heat source problems.
Reverse Markov inequality.
Reverse triangle inequality in Hilbert -modules.
Reverse weighted - norm inequalities in convolutions.
Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces.
Reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces.
Reverses of the triangle inequality in Banach spaces.
Revisited isoperimetric inequalities for the p-capacity and application to the muskat problem
Riemann average truth-value of Łukasiewicz formulas
Riemann Integral of Functions from ℝ into Real Banach Space
In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the...
Riemann Integral of Functions from R into n -dimensional Real Normed Space
In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].
Riemann Integral of Functions from R into R n
In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].
Riemann Integral of Functions from R into Real Normed Space
In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].
Riemann Integral of Functions R into C
In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].
Riemann type integrals for functions taking values in a locally convex space
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Riemann-Stieltjes Integral
In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described...
Riemann-type definition of the improper integrals
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
Riesz potential on the Heisenberg group.
Riesz potential operators and inverses via fractional centred derivatives.
Robust fractional adaptive control based on the strictly Positive Realness Condition
This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme...