Splitting Algorithms for the Sum of Two Nonlinear Operators

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

Download Full-text

A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

Journal of Geometric Analysis ◽

10.1007/s12220-021-00607-2 ◽

2021 ◽

Author(s):

Alessandro Goffi ◽

Francesco Pediconi

Keyword(s):

Maximum Principle ◽

Riemannian Manifolds ◽

Mean Curvature ◽

Strong Maximum Principle ◽

Second Order ◽

Fully Nonlinear Equations ◽

Nonlinear Operators ◽

Fully Nonlinear ◽

Second Order Equations ◽

Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Download Full-text

Splitting Algorithms for Equilibrium Problems and Inclusion Problems on Hadamard Manifolds

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2021.1933523 ◽

2021 ◽

pp. 1-38

Author(s):

Konrawut Khammahawong ◽

Poom Kumam ◽

Parin Chaipunya

Keyword(s):

Equilibrium Problems ◽

Hadamard Manifolds ◽

Inclusion Problems ◽

Splitting Algorithms

Download Full-text

Coupled fixed points of nonlinear operators with applications

Nonlinear Analysis ◽

10.1016/0362-546x(87)90077-0 ◽

1987 ◽

Vol 11 (5) ◽

pp. 623-632 ◽

Cited By ~ 240

Author(s):

Dajun Guo ◽

V. Lakshmikantham

Keyword(s):

Fixed Points ◽

Nonlinear Operators ◽

Coupled Fixed Points

Download Full-text

Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

Open Mathematics ◽

10.1515/math-2020-0049 ◽

2020 ◽

Vol 18 (1) ◽

pp. 858-872

Author(s):

Imed Kedim ◽

Maher Berzig ◽

Ahdi Noomen Ajmi

Keyword(s):

Banach Space ◽

Positive Solution ◽

Positive Definite ◽

Positive Cone ◽

Matrix Equations ◽

Ordered Banach Space ◽

Coincidence Points ◽

Nonlinear Operators ◽

Nonlinear Matrix

Abstract Consider an ordered Banach space and f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f(X)=g(X) has a positive solution, whenever f is strictly \alpha -concave g-monotone or strictly (-\alpha ) -convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.

Download Full-text