A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics by Gustavo Fernández-Torres

“…A geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton’s method and the convergence order of the new method is 1+2≈2.4142. …”
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Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem by Weidong Lv

“…By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. …”
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Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films by Anza Hafsa, Omar, Mandallena, Jean-Philippe

“…In particular, our results are consistent with one of the basic facts of nonlinear elasticity, namely the necessity of an infinite amount of energy to compress a finite volume of matter into zero volume. …”
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Some Reduction and Exact Solutions of a Higher-Dimensional Equation by Guangming Wang, Zhong Han

“…It can be verified that the reduced equation is a second order nonlinear ODE. Finally, some exact solutions of the Zakharov-Kuznetsov equation were constructed after solving the reduced equation.…”
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Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model by Minoru Tabata, Nobuoki Eshima

“…We extend the discrete nonlinear operator contained in the wage equation as a set-valued operator. …”
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Best Proximity Point Results for MK-Proximal Contractions by Mohamed Jleli, Erdal Karapınar, Bessem Samet

“…The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued function x↦d(x,Tx), where T belongs to a new class of contractive mappings. …”
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On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields by Michail P. Markakis, Panagiotis S. Douris

“…The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. …”
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Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative by A. K. Mishra, P. Gochhayat

“…The sharp bound for the nonlinear functional |a2a4−a32| is found. Several basic properties such as inclusion, subordination, integral transform, Hadamard product are also studied.…”
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Regularity for Variational Evolution Integrodifferential Inequalities by Yong Han Kang, Jin-Mun Jeong

“…We deal with the regularity for solutions of nonlinear functional integrodifferential equations governed by the variational inequality in a Hilbert space. …”
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Application of the Multistep Generalized Differential Transform Method to Solve a Time-Fractional Enzyme Kinetics by Ahmed Alawneh

“…This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. …”
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Algorithms for a System of General Variational Inequalities in Banach Spaces by Jin-Hua Zhu, Shih-Sen Chang, Min Liu

“…The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. …”
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Existence and Uniqueness of Positive Solutions for a Coupled System of Fractional Differential Equations by Hanying Feng, Xiaofeng Zhang

“…In this article, we investigate a boundary value problem for a coupled differential system of fractional order that the nonlinear term depends on the unknown functions as well as their lower order fractional derivatives. …”
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Development of Single-Longitudinal-Mode Selection Technology for Solid-State Lasers by Xuanpu Zhang, Zhihan Wang, Shi Liu, Siyu Gou, Rong Fan, Duo Jin, Zhenao Bai, Zhenxu Bai

“…Lasers with narrow linewidths and single frequencies are widely used in fields such as radar detection, nonlinear optics, and precision measurements. The demand for such lasers has promoted the rapid development of single-longitudinal-mode (SLM) selection technology. …”
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Integral invariant manifold method applied to a mathematical model of osteosarcoma by Ophir Nave

“…These interactions are described by nonlinear ordinary differential equations. By applying the MIM method, two critical dynamic variables (Cancer cells and Necrotic cells) were identified, providing insights into the dynamics of osteosarcoma over time during treatment.…”
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Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A by Dongjie Gao

“…We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). …”
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Gluing for the Einstein constraint equations by Corvino, Justin

“…Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint equations. …”
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Observation of a Class of Disturbance in Time Series Expansion for Fractional Order Systems by Yiheng Wei, Hamid Reza Karimi, Jinwen Pan, Qing Gao, Yong Wang

“…The stability of a special observer with the selected nonlinear weighted function and transient dynamics function is rigorously analyzed for slowly varying disturbance. …”
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Strong Convergence of Iterative Algorithm for a New System of Generalized H·,·-η-Cocoercive Operator Inclusions in Banach Spaces by Saud M. Alsulami, Eskandar Naraghirad, Nawab Hussain

“…Using the resolvent operator technique associated with H·,·-η-cocoercive operators, we suggest and analyze a new generalized algorithm of nonlinear set-valued variational inclusions and establish strong convergence of iterative sequences produced by the method. …”
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Decoupling the Stationary Navier-Stokes-Darcy System with the Beavers-Joseph-Saffman Interface Condition by Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

“…Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.…”
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Weak Sharp Minima in Set-Valued Optimization Problems by Ming-hao Jin, Jun-xiang Wang, Shu Xu

“…We present some sufficient and necessary conditions that a pair point is a weak ψ-sharp minimizer through the outer limit of set-valued map and develop the characterization of the weak ψ-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones in Studniarski (2007).…”
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