mean value theorem
On Generalized Flett's Mean Value Theorem
... A geometric interpretation of Theorem 1.1 states that if the curve y f x has a tangent at each point in a, b and fa fb, then there exists a point η ∈ a, b such that the tangent at η, fη is parallel to the x-axis. ...
8
Correction and Supplement to Approach for a Proof of Riemann Hypothesis by Second Mean Value Theorem
... The piece-wise constant Omega functions with equal interval lengths form a set of measure zero within the set of all piece-wise constant Omega functions and, moreover, within all Omega functions admitted by the second ...
15
Ostrowski and Trapezoid Type Inequalities Related to Pompeiu's Mean Value Theorem With Complex Exponential Weight
... Abstract. We present some inequalities of Ostrowski and trapezoid type with complex exponen- tial weight, for complex-valued absolutely continuous functions. These inequalities are related to Pompeiu’s mean ...
18
A survey on Ostrowski type inequalities related to Pompeiu's mean value theorem
... In order to provide another approximation of the integral mean, by making use of the Pompeiu’s mean value theorem, the author proved the following result: Theorem 1.4 (Dragomir, 2005 ...
35
Approach to a Proof of the Riemann Hypothesis by the Second Mean Value Theorem of Calculus
... respect to the multi-valuedness. This is better to see in case of the modified Bessel functions for which the curves vanish less rapidly with increasing y as we intend to show at another place. All these considerations ...
51
On a functional equation related to a generalization of Flett's mean value theorem
... Lagrange mean value theorem to ask the question of which functions attained their mean value at a prescribed point c ∈ (a,b), in par- ticular, at the midpoint c = (a + ...the ...
5
Flett's mean value theorem in topological vector spaces
... 1. Introduction. In 1958, Flett proved that if f : [a, b] → R is differentiable on [a, b] and satisfies f (a) = f (b), then there exists η in the open interval (a, b) such that f (η) − f (a) = (η − a)f (η) [3]. Flett’s ...
6
The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel
... the mean value theorem and Taylor’s theorem for derivatives defined in terms of a Mittag–Leffler ...Taylor’s theorem in the ABC context appear different from classical and previous results, ...
11
An axiomatic integral and a multivariate mean value theorem
... general mean value theorem for n-dimensional functions is obtained directly from the fact that the normalized integral should belong to the convex hull of the set of values of the ...following ...
11
Mean value theorem for integrals and its application on numerically solving of Fredholm integral equation of second kind with Toeplitz plus Hankel Kernel
... The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and ...
10
AMS Subject Classification: Primary 39B82; Secondary 39B22; 26D10. Key Words: Hyers-Ulam stability; mean value theorem; Lagrange’s mean value point; two-
... In Section 3, we prove the Hyers-Ulam stability of two-dimensional Lagrange’s mean value points. The main result of this paper is an extension and a generalization of the previous work [6, Theorem ...
10
M53 Lec4.6 Volume by Slicing and Mean Value Theorem for Integrals.pdf
... perpendicular to the y -axis is an isosceles right triangle with one leg lying on. the base of the solid[r] ...
152
Ostrowski and Trapezoid type inequalities related to Pompeiu's mean value theorem
... In this paper, we give refinements of the inequalities in Theorem 7 in Section 2. We also present similar results for trapezoid inequalities in Section 3. In Section 4, we apply these inequalities to compare the ...
24
General Integral Control Design via Singular Perturbation Technique
... technique, mean value theorem, stability theorem of interval matrix and Lyapunov ...5) Theorem 1 is not suspended in midair but is established on a solid ...
10
Observer Design for a Class of Nonlinear Discrete Time Systems: Real Time Application to the One link Flexible Joint Robot
... This paper demonstrates the observer design for large class of nonlinear discrete time systems. The use of the differential mean value theorem (DMVT) allows transforming the nonlin- ear error ...
6
Australian Journal of Basic and Applied Sciences
... In this paper, new generalizations of Weierstrass inequality are established by using principles of mathematical analysis as the principle of Mean Value Theorem.. PRELIMINARIES AND LEM[r] ...
7
UNIFIED NOTATION FOR INTEGRALS. Frequently we shall discuss results
... DERIVATION OF THE DIFFERENTIATION THEOREMS. Here is the derivation based upon the Mean Value Theorem(s). Throughout this discussion the point p in the domain D will remain fixed, and to simplify ...
6
Some Grüss-type results via Pompeiu’s-like inequalities
... Pachpatte, B.G.: On Grüss like integral inequalities via Pompeiu’s mean value theorem. Peˇcari´c, J.; Ungar, Š.: On an inequality of Ostrowski type[r] ...
12
On a sum analogous to Dedekind sum and its mean square value formula
... and mean value distribution properties of C(h, ...the mean value theorem of Dirichlet L-functions to prove the following main ...
9
M53 Lec3.1 MVT and Relative Extrema.pdf
... The Mean Value Theorem and Relative Extrema.. Mathematics 53.[r] ...
200