On the convergence of the three-step iteration process in the class of quasi-contractive operators.
On the convergence of two-step Newton-type methods of high efficiency index
We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.
On the convergence theorems for a countable family of Lipschitzian pseudocontraction mappings in Banach spaces.
On the discreteness of the spectra of the Dirichlet and Neumann -biharmonic problems.
On the double critical-state model for type-II superconductivity in 3D
In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...
On the equivalence of Mann and Ishikawa iteration methods.
On the existence and convergence of approximate solutions for equilibrium problems in Banach spaces.
On the existence of multiple solutions for a nonlocal BVP with vector-valued response
The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.
On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem.
On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method.
On the existence of solution of the equation and a generalized coincidence degree theory. II.
On the existence of solution of the equation and a generalized coincidence degree theory. I.
On the existence of the price equilibrium by different methods
We have given several proofs on the existence of the price equilibrium --- via variational inequality --- via degree theory and via Brouwer's theorems.
On the existence of weak solutions for some quasilinear elliptic variational boundary value problems at resonance
On the existence theorems of Kantorovich, Miranda and Borsuk.
On the fixed point index of non-compact mappings
On the generalized nonlinear quasivariational inclusions
On the Halley method in Banach spaces
We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.
On the Hénon equation : asymptotic profile of ground states, I
On the ishikawa iteration process in Hilbert spaces.