Iterative algorithms for a finite family of equilibrium problems and fixed point problem in an Hadamard space
Chinedu Izuchukwu, O.T. Mewomo · Fixed Point Theory · 2023
The main purpose of this paper is to introduce a viscosity-type proximal point algorithm for approximating a common solution of a finite family of equilibrium problems and fixed point problem for a certain class of nonspreading-type mappings recently introduced by Phuengrattana [Applied General Topology 18(2017), 117-129].We further establish a strong convergence of our proposed algorithm to a common solution of a finite family of equilibrium problems which is also a fixed point of this class of mappings and a unique solution of some variational inequality problems in an Hadamard space.We also analyse the asymptotic behaviour of the sequence generated by a viscosity-type algorithm and extend the analysis to approximate a common solution of a finite family of equilibrium problems in an Hadamard space.Furthermore, we applied our results to solve some optimization problems in Hadamard spaces.