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Existence and approximation results for SKC mappings in Busemann spaces

100%

Khan S. H., Abbas M., Nazir T.

Waves, Wavelets and Fractals

2017

tom 3

nr 1

48-60

In this paper, we first discuss some properties of SKC mappings in the context of Busemann spaces and obtain a demiclosedness principle.We then prove the existence and approximation results for SKC mappings in a uniformly convex Busemann space. At the end, we give a numerical example in support of our main result. This example also shows that our iterative process is faster than some well-known iterative processes even for SKC mappings. Our results are certainly more general than many results in the contemporary literature.

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Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces

86%

Kozlowski W. M.

Commentationes Mathematicae

2014

tom 54

nr 2

Let $C$ be a convex compact subset of a uniformly convex Banach space. Let $\{T_t\}_{t \geq0}$ be a strongly-continuous nonexpansive semigroup on $C$. Consider the iterative process defined by the sequence of equations $$x_{k+1} =c_k T_{t_{k+1}}(x_{k+1})+(1-c_k)x_k.$$ We prove that, under certain conditions on $\{c_k\}$ and $\{t_k\}$, the sequence $\{x_k\}_{n=1}^\infty$ converges strongly to a common fixed point of the semigroup $\{T_t\}_{t \geq0}$. There are known results on convergence of such iterative processes for nonexpansive semigroups in Hilbert spaces and Banach spaces with the Opial property, and also weak convergence results in Banach spaces that are simultaneously uniformly convex and uniformly smooth. In this paper, we do not assume the Opial property or uniform smoothness of the norm.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Waves, Wavelets and Fractals

1 Abbas M.

1 Khan S. H.

1 Kozlowski W. M.

1 Nazir T.

1 2017

1 2014

Wyniki wyszukiwania

Existence and approximation results for SKC mappings in Busemann spaces

Strong convergence of implicit iteration processes for nonexpansive semigroups in Banach spaces