Results 21 to 30 of about 2,683,293 (266)
Mean Value Theorems for Vector Valued Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1965 The object of this paper is to give a generalisation to vector valued functions of the classical mean value theorem of differential calculus. In that theorem we havefor some c in the open interval a, b when f is a real valued function which is continuous on the closed interval a, b and differentiable on the open interval.
openaire +2 more sources
Mean-value theorem for vector-valued functions [PDF]
Mathematica Bohemica, 2012 Summary: For a differentiable function \(f\: I\rightarrow \mathbb {R}^k\), where \(I\) is a real interval and \(k\in \mathbb {N}\), a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence of a mean \(M\: I^2\rightarrow I\) such that \[ f(x)-f(y)=(x-y)f'(M(x,y)),\; x,y\in I, \] are given ...
openaire +1 more source
On the Mean Value of Multiplicative Functions
Journal of Number Theory, 1995 The author generalizes the known mean value theorems for multiplicative functions \(f\) of Delange, Elliot, Daboussi and Indlekofer, but not of Heppner.
openaire +1 more source
An asymptotic formula for the gcd-sum function of Jordan's totient function
四川大学学报. 自然科学版, 2021 Let $\gcd(k, j)$ denote the greatest common divisor of the positive integers $k$ and $j$, $r$ be any fixed positive integer. In this paper, by using the identity of Kiuchi on $M_r(x; f)$ together with analytic method, we present asymptotic formulas of ...
LI Lin-Feng, TAN Qian-Rong, CHEN Long
doaj
Mean Values of Products of L-Functions and Bernoulli Polynomials
Mathematics, 2018 Let m 1 , ⋯ , m r be nonnegative integers, and set: M r = m 1 + ⋯ + m r . In this paper, first we establish an explicit linear decomposition of: ∏ i = 1 r B m i ( x ) m i !
Abdelmejid Bayad, Daeyeoul Kim
doaj +1 more source
Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Background Therapeutic apheresis (TA) is an established treatment modality for hematologic, neurologic, and immunologic disorders, yet access remains severely limited in sub‐Saharan Africa. Donor apheresis, including platelet apheresis collection from healthy donors, represents an important complementary modality supporting blood product ...
Nosa Bazuaye +33 more
wiley +1 more source
ON TWO-SIDED UNIDIRECTIONAL MEAN VALUE INEQUALITY IN A FRÉCHET SMOOTH SPACE
Ural Mathematical Journal, 2023 The paper is devoted to a new unidirectional mean value inequality for the Fréchet subdifferential of a continuous function. This mean value inequality finds an intermediate point and localizes its value both from above and from below; for this reason ...
Dmitry V. Khlopin
doaj +1 more source
Functional Equalities and Some Mean Values
Journal of Mathematical Analysis and Applications, 2000 Some generalizations of the results of \textit{Y.-H. Kim} [J. Math. Anal. Appl. 235, No.~2, 598-607 (1999; Zbl 0954.26004)] are given. For example, it is proved that if \( h:\mathbb{R}^{+}\rightarrow \mathbb{R}\) is a strictly monotonic function and \(M\) is a mean value, then there exists a number \(T>1\) such that ...
Abramovich, Shoshana, Pec̆arić, Josip
openaire +2 more sources
On the mean values of the Chebyshev function and their applications
Chebyshevskii sbornik, 2021 When solving a number of problems in prime number theory, it is sufficient that $t(x;q)$ admits an estimate close to this one. The best known estimates for $t(x;q)$ previously belonged to G.~Montgomery, R.~Vaughn, and Z.~Kh.~Rakhmonov. In this paper we obtain a new estimate of the form $$ t(x;q)=\sum_{χ\bmod q}\max_{y\leq x}|ψ(y,χ)|\ll x{\mathscr{L ...
Rakhmonov, Zarullo Khusenovich +1 more
openaire +3 more sources
Therapeutic Apheresis and Dialysis, EarlyView.ABSTRACT Introduction This study investigated the safety and efficacy of single‐needle Rheocarna therapy for chronic limb‐threatening ischemia (CLTI) with wounds. Methods Six patients with CLTI involving ulcers unresponsive to revascularization underwent single‐needle Rheocarna treatment.
Yasutaka Yamauchi +9 more
wiley +1 more source