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New fixed points of mixed monotone operators with applications to nonlinear integral equations. [PDF]
PLoS ONEIn this paper, first we recall and present some basic results about cone and partial order within the framework of Banach spaces. Next, by means of the properties of cone and monotone iterative techniques, some new fixed point theorems of mixed monotone ...
Shaoyuan Xu +3 more
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Algebraic Systems with Positive Coefficients and Positive Solutions
Mathematics, 2022 The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients.
Ana Maria Acu +2 more
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A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations
Mathematics, 2020 The goal of this paper is to extend the modified Hestenes-Stiefel method to solve large-scale nonlinear monotone equations. The method is presented by combining the hyperplane projection method (Solodov, M.V.; Svaiter, B.F.
Zhifeng Dai, Huan Zhu
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Abstract and Applied Analysis, 2020 Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses.
Mathew O. Aibinu +2 more
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Monotone method for Riemann-Liouville multi-order fractional differential systems [PDF]
Opuscula Mathematica, 2016 In this paper we develop the monotone method for nonlinear multi-order \(N\)-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders \(q_i\) where \(0 \lt q_i \lt 1\).
Zachary Denton
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Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations [PDF]
, 2013 This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D.
Feng, Xiaobing +2 more
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Results in Applied Mathematics, 2019 In this article, we propose a three-term conjugate gradient projection algorithm for solving constrained monotone nonlinear equations. The global convergence of the algorithm was established under suitable assumptions.
Auwal Bala Abubakar +2 more
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Positive Decreasing Solutions of Higher-Order Nonlinear Difference Equations
Advances in Difference Equations, 2010 It is shown that the decay rates of the positive, monotone decreasing solutions approaching the zero equilibrium of higher-order nonlinear difference equations are related to the positive characteristic values of the corresponding linearized equation. If
B. Krasznai, I. Győri, M. Pituk
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Mathematics, 2019 In this article, we propose a modified self-adaptive conjugate gradient algorithm for handling nonlinear monotone equations with the constraints being convex. Under some nice conditions, the global convergence of the method was established.
Auwal Bala Abubakar +3 more
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Mathematics, 2019 One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations.
Auwal Bala Abubakar +4 more
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