A hybrid proximal point algorithm for finding minimizers and fixed points in CAT(0) spaces

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Authors

Ugwunnadi, Godwin Chidi
Khan, Abdul Rahim
Abbas, Mujahid

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Springer

Abstract

We introduce a hybrid proximal point algorithm and establish its strong convergence to a common solution of a proximal point of a lower semi-continuous mapping and a fixed point of a demicontractive mapping in the framework of a CAT(0) space. As applications of our new result, we solve variational inequality problems for these mappings on a Hilbert space. Illustrative example is given to validate theoretical result obtained herein.

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Keywords

Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping

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Citation

Ugwunnadi, G.C., Khan, A.R. & Abbas, M. J. A hybrid proximal point algorithm for finding minimizers and fixed points in CAT(0) spaces. ournal of Fixed Point Theory and Applications. (2018) 20: 82. https://doi.org/10.1007/s11784-018-0555-0.