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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.
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Generalized Petrovic’s Inequalities for Coordinated Exponentially m-Convex Functions
International Journal of Analysis and Applications, 2021 In this paper, we introduce a new class of convex function, which is called coordinated exponentially m-convex functions. Some new Petrovic’s type inequalities for exponentially m-convex functions and coordinated exponentially m-convex functions are ...
Wasim Iqbal +3 more
doaj
On Some Cauchy Type Mean-Value Theorems with Applications
Communications in Advanced Mathematical SciencesSome Cauchy-type mean-value theorems for Chebychev’s inequality, Steffensen’s inequality, midpoint rule, and Simpson’s rule are presented. Furthermore, we give some applications for the obtained results using the exponential and logarithmic functions ...
Uğur Selamet Kırmacı
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Generalized $1$-harmonic Equation and The Inverse Mean Curvature Flow
, 2010 We introduce and study generalized $1$-harmonic equations (1.1). Using some ideas and techniques in studying $1$-harmonic functions from [W1] (2007), and in studying nonhomogeneous $1$-harmonic functions on a cocompact set from [W2, (9.1)] (2008), we ...
Ai-Nung Wang +20 more
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Multimodal Data‐Driven Microstructure Characterization
Advanced Engineering Materials, EarlyView.A self‐consistent autonomous workflow for EBSP‐based microstructure segmentation by integrating PCA, GMM clustering, and cNMF with information‐theoretic parameter selection, requiring no user input. An optimal ROI size related to characteristic grain size is identified.
Qi Zhang +4 more
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Analyzing Electronic Excitations and Exciton Binding Energies in Y6 Films
Advanced Functional Materials, EarlyView.The Y6 molecule is used for increasing the efficiency of organic solar cells. The exciton binding energy is calculated for ensembles of Y6 molecules that are representative of the typically used films. The calculations show that the excitons typically spread out over many molecules.
Sahar Javaid Akram +2 more
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Cubo, 2022 In this paper we introduce an operator that can be thought as a derivative of variable order, i.e. the order of the derivative is a function. We prove several properties of this operator, for instance, we obtain a generalized Leibniz‘s formula, Rolle and
René Erlín Castillo, Babar Sultan
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Stacking‐Engineered Magnonic Topology and Transport in Honeycomb Homobilayers
Advanced Functional Materials, EarlyView.ABSTRACT Topological magnons have emerged as a promising platform for dissipationless bosonic transport. However, a straightforward and effective strategy to engineer such topological states in real materials has yet to be fully realized. Here, a general scheme for controlling magnonic topological states via stacking engineering in van der Waals ...
Xiaoran Feng +6 more
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Some Generalizations of the Jensen-Type Inequalities with Applications
Axioms, 2022 Motivated by some results about reverses of the Jensen inequality for positive measure, in this paper we give generalizations of those results for real Stieltjes measure dλ which is not necessarily positive using several Green functions.
Mirna Rodić
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Some Mean-Value Theorems of the Cauchy Type [PDF]
, 2006 2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05Some mean-value theorems of the Cauchy type, which are connected with Jensen’s inequality, are given in [2] in discrete form and in [5] in integral form.
Pecaric, Josip +2 more
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