Auxiliary principle technique and iterative algorithm for a perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems.
In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems, and then by using the celebrated Fan-KKM technique, we establish the existence and uniqueness of solutions of the perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems. By deploying an auxiliary principle technique and an existence result, we formulate an iterative algorithm for solving the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems. Lastly, we study the strong convergence analysis of the proposed iterative sequences under monotonicity and some mild conditions. These results are new and generalize some known results in this field.
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Mijanur
M
Rahaman
Department of Information Management, and Innovation Centre for Big Data and Digital Convergence, Yuan Ze University, Chung-Li, 32002 Taiwan.
Chin-Tzong
CT
Pang
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Mohd
M
Ishtyak
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002 India.
Rais
R
Ahmad
algorithm; convergence; perturbed system; quasi-equilibrium-like