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Section 9 includes a convergence, approximation, and periodic point of Nadler-type result with its proof.
It is widely recognized that the existence, uniqueness, convergence, approximation, and fixed point result concerning single-valued contractions in complete metric spaces of Banach [14] (see also Caccioppoli [15]) deeply influenced the direction of fixed point theory.
In this section, we deal with a strong convergence approximation scheme for finding a common element of the set of common fixed points of a representation of nonexpansive mappings.
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A strict theoretical analysis is carried out as regards the convergence and approximation properties of the iterative scheme, and the related stability and approximation properties of the nonlinear fully implicit finite difference (FIFD) scheme.
These methods cannot always guarantee the convergence of approximation series.
In 2010, Ibrahim[6] introduced Stancu-Chlodowsky Polynomials and investigated convergence and approximation properties of these operators.
Until the study of Gadjiev and Orhan [17], there was no study related to statistical convergence and approximation theory.
Some properties of the convergence and approximation for some Bézier-type operators have been studied (cf. [2 6]), but there are other aspects that have not yet been considered.
More precisely, the subject of this paper is the constructions of contractions and weak contractions of Leader type and the study of convergence, existence, approximation, periodic point, fixed point, and uniqueness properties of these contractions and weak contractions in quasi-triangular spaces ((X,mathcal{P}_{C mathcal{A}})).
HDM provides us with a convenient way to control the convergence of approximation series without adapting h, as in the case of [ 24] which is a fundamental qualitative difference in analysis between HDM and other methods [ 29– 34, 34– 34].
The convergence of approximations to a weak solution of the original problem is proved.
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