Some Fixed Point Theorems for Countably Condensing
Abdul-Majeed Al-izeri,
Ahmed Al-Haysah
Issue:
Volume 9, Issue 2, April 2023
Pages:
10-13
Received:
25 July 2023
Accepted:
11 September 2023
Published:
24 September 2023
Abstract: Our aim in this article is to establish the principles results of a fixed point theorems for multivalued mappings of Krasnoselskii type setting in general classes Mönch’s type. We seek to do that, we introduce and recall some theorems to aid our study. The beginning of this work has been introduced some properties of the measure of weak noncompactness under the weak topology and the definitions of countably condensing operators. We have shown that the operator H(S) is relatively weakly compact by using some properties of weak topology. We investigate that all hypotheses guarantee that the operator (B + H)(S) is relatively weakly compact and than simply to apply Himmelberg’s theorem in Banach spaces. We extended two fixed point theorems for weakly sequentially upper semicontinuous mappings subjected the perturbation map satisfies the Mönch’s type and we obtain our results in the second theorem with a less restrictive hypothesis. Using abstract measures of weak noncompactness, these results are applied to derive some fixed point theorems for a weakly sequentially upper semicontinuous countably µ-condensing multivalued mappins.
Abstract: Our aim in this article is to establish the principles results of a fixed point theorems for multivalued mappings of Krasnoselskii type setting in general classes Mönch’s type. We seek to do that, we introduce and recall some theorems to aid our study. The beginning of this work has been introduced some properties of the measure of weak noncompactn...
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Research Article
Convergence Analysis of Viscosity Implicit Rules of Asymptotically Nonexpansive Mappings in Hilbert Spaces
Furmose Mendy,
John T Mendy,
Jatta Bah,
Gabriel Mendy
Issue:
Volume 9, Issue 2, April 2023
Pages:
14-22
Received:
3 May 2023
Accepted:
18 May 2023
Published:
1 November 2023
Abstract: Viscosity’s implicit algorithm for finding a common element of the set of fixed points for nonlinear operators and the set of solutions of variational inequality problems have been investigated by many authors in different settings in Hilbert and Banach space. In most cases, they consider the following study of viscosity implicit double midpoint, generalized viscosity in the class of nonexpansive and asymptotically nonexpansive mappings. The implicit midpoint rule can effectively solve ordinary differential equations. Meanwhile, many authors have used viscosity iterative algorithms for finding common fixed points for nonlinear operators and solutions of variational inequality problems. Recently, the convergence rate and comparison viscosity implicit iterative algorithm has been studied widely. Under suitable conditions imposed on the control parameters, it is shown in this paper that certain two implicit iterative sequences {ωn} and {ξn} converge to the same fixed point of an asymptotically nonexpansive mapping in Hilbert spaces without comparison. It is also proven that {ωn} and {ξn} converge strongly to the same solution, which also solves the variational inequality problem. The results presented in this paper improve and extend some recent corresponding results in the literature.
Abstract: Viscosity’s implicit algorithm for finding a common element of the set of fixed points for nonlinear operators and the set of solutions of variational inequality problems have been investigated by many authors in different settings in Hilbert and Banach space. In most cases, they consider the following study of viscosity implicit double midpoint, g...
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