THE MEAN VALUE THEOREM ¤ 153
The Mean Value Theorem
... Thus the given equation has a root. Now we show that this root is unique, that is there are no other roots. We will prove it by a contradiction. Assume to the contrary that the equation x 5 + 7x − 2 = 0 has at least two ...
5
Intermediate Value Theorem, Rolle s Theorem and Mean Value Theorem
... Intermediate Value Theorem, Rolle’s Theorem and Mean Value Theorem February 21, 2014 In many problems, you are asked to show that something exists, but are not required to give a ...
5
On Generalized Flett's Mean Value Theorem
... Mean value theorems play an essential role in ...the mean value theorem due to Rolle is well ...known. Theorem 1.1 Rolle’s mean value ...
8
A MEAN VALUE THEOREM FOR METRIC SPACES
... To conclude, this paper is organized in the following sequence: in Section 2, we discuss the basic properties associated with sets that describes the regularity of a given function defined on a metric space. These sets ...
18
An axiomatic integral and a multivariate mean value theorem
... Abstract In order to investigate minimal sufficient conditions for an abstract integral to belong to the convex hull of the integrand, we propose a system of axioms under which it happens. If the integrand is a continuous ...
11
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
Flett's mean value theorem in topological vector spaces
... 2000 Mathematics Subject Classification. 58C20, 26E20, 46G05. 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 ...
6
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
On a functional equation related to a generalization of Flett's mean value theorem
... In this paper, we characterize all the functions that attain their Flett mean value at a particular point between the endpoints of the interval under consideration.. These functions turn[r] ...
5
Section 3.7. Rolle s Theorem and the Mean Value Theorem. Difference Equations to Differential Equations
... The Mean Value Theorem, of which Rolle’s Theorem is a special case, says that if f is differentiable on an interval, then there is some point in that interval at which the instantaneous rate ...
13
Approach to a Proof of the Riemann Hypothesis by the Second Mean Value Theorem of Calculus
... second mean-value theorem is applicable (function Ω ( ) u positively semi-definite and non-increasing) may possess zeros only on the imaginary ...second mean-value theorem was ...
51
Ostrowski and Trapezoid type inequalities related to Pompeiu's mean value theorem
... We also refer the readers to the related results and their applications to the special means by Dragomir [14]. In this paper, we give refinements of the inequalities in Theorem 7 in Section 2. We also present ...
24
A survey on Ostrowski type inequalities related to Pompeiu's mean value theorem
... Abstract. In this paper we survey some recent results obtained by the au- thor related to Pompeiu’s mean value theorem and inequality. Natural appli- cations to Ostrowski type inequalities that play ...
35
Correction and Supplement to Approach for a Proof of Riemann Hypothesis by Second Mean Value Theorem
... second mean-value theorem of calculus and the majority of other Omega functions in the suppositions, but makes their deri- vation ...the mean-value functions and the application to ...
15
Ostrowski and Trapezoid Type Inequalities Related to Pompeiu's Mean Value Theorem With Complex Exponential Weight
... WITH COMPLEX EXPONENTIAL WEIGHT P IETRO C ERONE , S EVER S. D RAGOMIR AND E DER K IKIANTY (Communicated by A. Agli´c Aljinovi´c) Abstract. We present some inequalities of Ostrowski and trapezoid type with complex ...
18
AMS Subject Classification: Primary 39B82; Secondary 39B22; 26D10. Key Words: Hyers-Ulam stability; mean value theorem; Lagrange’s mean value point; two-
... a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two- dimensional Lagrange’s mean value points (η, ξ) which satisfy the equation, f (u, v) − f (p, q) = (u − p)f x (η, ξ) + (v − ...
10
An existence theorem for restrictions on the mean in the presence of a restriction on the dispersion
... “restriction” for one border and the “restriction” for another border constitute the “restrictions” for the borders. Here, the non-zero dispersion of the function models the consequence of existence of real scattering. ...
46
Majority stable production equilibria : a multivariate mean shareholders theorem
... present value of the production plans that are not in the span of the ¯nancial structure: to discount future income streams, they use shadow prices that can be ...
38
Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem II. High dimensional problems
... It must be emphasized that for simplicity of computations, c(x) in the mean value theorem, was taken as a constant. It remains a matter of further research (as an open problem) to modify the ...
11
,…,Y According to the extreme value theorem [2],
... the mean, while the third governs the shape of the tail of the distribution and it is probably the most important parameter since larger values correspond to fatter tailed ...
5