A Fixed Point Theorem for Systems of Nonlinear Operator Equations and Applications to $$(p_1, p_2)$$ ( p 1 , p 2 ) -Laplacian System

2018 ◽  
Vol 15 (2) ◽  
Author(s):  
Yumei Zou ◽  
Guoping He
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations

scholarly journals Fixed Point Theorems on Nonlinear Binary Operator Equations with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Baomin Qiao
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Order Theory ◽  
Iteration Theory ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Monotone Iteration ◽  
Binary Operator

The existence and uniqueness for solution of systems of some binary nonlinear operator equations are discussed by using cone and partial order theory and monotone iteration theory. Furthermore, error estimates for iterative sequences and some corresponding results are obtained. Finally, the applications of our results are given.

scholarly journals Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mathew Aibinu ◽  
Surendra Thakur ◽  
Sibusiso Moyo
Keyword(s):  
Fixed Point ◽  
Nonlinear Operator ◽  
Monotone Mappings ◽  
Operator Equations ◽  
Fredholm Type ◽  
Nonlinear Operator Equations ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings ◽  
Implicit Iterative Algorithm ◽  
Strictly Pseudocontractive Mappings

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ-strictly pseudocontractive mappings, solution of α-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type.

scholarly journals Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonlinear Operator ◽  
Wage Equation ◽  
Short Run ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

Each short-run equilibrium of the Dixit-Stiglitz-Krugman model is defined as a solution to the wage equation when the distributions of workers and farmers are given functions. We extend the discrete nonlinear operator contained in the wage equation as a set-valued operator. Applying the Kakutani fixed-point theorem to the set-valued operator, under the most general assumptions, we prove that the model has a short-run equilibrium.

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