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2 2015

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Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems

Shehu Y., Ogbuisi F. U.

Journal of Applied Analysis

2015

Vol. 21, nr 2

63--77

In this paper we propose an iterative algorithm based on the hybrid method in mathematical programming for approximating a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which also solves a finite system of equilibrium problems in a reflexive real Banach space.We further prove that our iterative sequence converges strongly to a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which is also a common solution to a finite system of equilibrium problems. Our result extends many recent and important results in the literature.

Multiwavelets and multiwavelet packets of Legendre functions in the direct method for solving variational problems

Jarczewska K., Glabisz W., Zielichowski-Haber W.

Archives of Civil and Mechanical Engineering

2015

Vol. 15, no. 1

1--10

A numerical technique for solving the linear problems of the calculus of variations is presented in this paper. Multiwavelets and multiwavelet packets of Legendre functions are used as basis functions in the Ritz method of formulation. An operational matrix of integration of multiwavelets and multiwavelet packets is introduced and is used to reduce the calculus of variation problem to the solution of the system of algebraic equations. The algorithm is applied to the analysis of mechanic problems which are formulated as func-tionals. Two examples are considered in this paper. The first example concerns the stability problem of a Euler–Bernoulli beam and the second one presents the calculation of the extreme value of the functional which defines the potential energy of an elastic string. The presented method yields the approximate solutions which are convergent to accurate results.