A unifying semilocal convergence theorem for Newton-like methods in Banach space.
A unifying theorem on Newton's method in a Banach space with a convergence structure under weak assumptions.
A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.
A viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in Hilbert spaces.
A viscosity of Cesàro mean approximation methods for a mixed equilibrium, variational inequalities, and fixed point problems.
A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition on the inertial term. Finally, we provide...
A weak convergence theorem for total asymptotically pseudocontractive mappings in Hilbert spaces.
A weaker affine covariant Newton-Mysovskikh theorem for solving equations
The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples...
Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.
Alcune osservazioni sul rango numerico per operatori non lineari
We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984).
Algorithms of common solutions to generalized mixed equilibrium problems and a system of quasivariational inclusions for two difference nonlinear operators in Banach spaces.
Almost stable iteration schemes for local strongly pseudocontractive and local strongly accretive operators in real uniformly smooth Banach spaces.
An algorithm based on resolvent operators for solving positively semidefinite variational inequalities. (An algorithm based on resolvant operators for solving positively semidefinite variational inequalities.)
An algorithm for finding a common solution for a system of mixed equilibrium problem, quasivariational inclusion problem, and fixed point problem of nonexpansive semigroup.
An application of hybrid steepest descent methods for equilibrium problems and strict pseudocontractions in Hilbert spaces.
An approximation method for continuous pseudocontractive mappings.
An approximation of solutions of variational inequalities.
An Error Analysis for the Secant Method.
An existence and uniqueness result for semilinear equations with Lipschitz nonlinearity.
An extension of the auxiliary problem principle to nonsymmetric auxiliary operators