A hybrid proximal point algorithm for finding minimizers and fixed points in CAT(0) spaces
04 Jun 2018We 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.
| Authors: | Ugwunnadi, Godwin Chidi, Khan, Abdul Rahim, Abbas, Mujahid |
| Institution: | University of Pretoria |
| Keywords: | Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping, Proximal point, CAT(0) space, Strong convergence, △ convergence, Fixed point, Demicontractive mapping |