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1

Convergence theorem for a finite family of asymptotically demicontractive multi-valued mappings in CAT(0) spaces

Ugwunnadi Godwin C., Mewomo Oluwatosin T., Izuchukwu Chinedu

Journal of Applied Analysis

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2020

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Vol. 26, nr 1

117--130

EN

In this paper, we introduce the class of asymptotically demicontractive multivalued mappings and establish a strong convergence theorem of the modified Mann iteration to a common fixed point of a finite family of asymptotically demicontractive multivalued mappings in a complete CAT(0) space. We also give a numerical example of our iterative method to show its applicability.

2

Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Abbas Mujahid, Iqbal Hira, de la Sen Manuel

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

347--360

EN

We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete R-trees without the endpoint condition.

3

On the proximal point algorithm and demimetric mappings in CAT(0) spaces

Aremu K. O., Izuchukwu C., Ugwunnadi G. C., Mewomo O. T.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

277--294

EN

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces. We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore, we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

4

Noncyclic Meir-Keeler contractions and best proximity pair theorems

Gabeleh M., Markin J.

Demonstratio Mathematica

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2018

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Vol. 51, nr 1

171--181

EN

In this article, we consider the class of noncyclic Meir-Keeler contractions and study the existence and convergence of best proximity pairs for such mappings in the setting of complete CAT(0) spaces. We also discuss asymptotic pointwise noncyclic Meir-Keeler contractions in the framework of uniformly convex Banach spaces and generalize a main result of Chen [Chen C. M., A note on asymptotic pointwise weaker Meir-Keeler type contractions, Appl. Math. Lett., 2012, 25, 1267-1269]. Examples are given to support our main results.

5

Convergence of modified s-iteration process for two asymptotically quasi-nonexpansive type mappings in CAT(0) spaces

Saluja G. S.

Demonstratio Mathematica

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2016

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Vol. 49, nr 1

107--118

EN

The purpose of this paper is to study convergence of a newly defined modified S-iteration process to a common fixed point of two asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space. We give a sufficient condition for convergence to a common fixed point and establish some strong convergence theorems for the said iteration process and mappings under suitable conditions. Our results extend and improve many known results from the existing literature.