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Some preliminary results and notions are given in Section 2, while the main results about a unified convergence criterion are presented in Section 3.
Under a generalized L-average Lipschitz condition of the differential of f, we establish a unified convergence criterion of Newton's method.
Recently, a new unified convergence analysis for (C^{1} -conforming FEs, classical nonconforming FEs, and discontinuous FEMs for problem (1} -conforminged in [17, 18].
Furthermore, in [14], Li and Wang extended the generalized L-average Lipschitz condition (introduced in [6]) to Riemannian manifolds and established a unified convergence criterion of Newton's method on Riemannian manifolds.
Gradient schemes is a framework which enables the unified convergence analysis of many different methods–such as finite elements (conforming, non-conforming and mixed) and finite volumes methods for 2nd order diffusion equations.
The purpose of the present paper is to establish a unified convergence criterion for Newton's method (independent of the connection) on Lie groups under a generalized L-average Lipschitz condition.
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Motivated and inspired by the recent research work in this direction, we introduce the following finite step relaxed hybrid steepest-descent algorithm for finding approximate solutions of VI( and aim to unify the convergence results of this kind of methods. Algorithm 1.1. Let,, for, and take fixed numbers,. Starting with arbitrarily chosen initial points, compute the sequences such that (1.3).
The heart of that is unified communications essentially the convergence of voice, data and video.
Using ideals, Kostyrko et al.[17] defined I Open image in new window-convergence, a stronger convergence in a metric space, whereas Dass et al.[18] unified this idea with statistical convergence for real sequences.
After the development of fluid dynamics and its application to atmospheric motion, various definitions were gradually unified (Simpson 1947, who used the term "intertropical convergence").
Quite recently, Das et al. [26] unified these two approaches to introduce new concepts of I-statistical convergence, I-lacunary statisticonvergenceence and investigated some of their consequences.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com