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1

Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

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

Journal of Applied Analysis

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2020

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Vol. 26, nr 2

221--229

EN

In this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in p-uniformly convex metric spaces, and prove both Delta-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete p-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

2

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.

3

On θ-generalized demimetric mappings and monotone operators in Hadamard spaces

Ogwo Grace N., Izuchukwu Chinedu, Aremu Kazeem O., Mewomo Oluwatosin T.

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

95--111

EN

Our main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.