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Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm

Lateef O. Jolaoso, Oluwatosin T. Mewomo (2020)

Commentationes Mathematicae Universitatis Carolinae

This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences and also...

Approximation methods for solving the Cauchy problem

Cristinel Mortici (2005)

Czechoslovak Mathematical Journal

In this paper we give some new results concerning solvability of the 1-dimensional differential equation y ' = f ( x , y ) with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if f is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution....

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