Student Number
27333
Degree
Master of Science in Mathematics
Department
Department of Mathematical Sciences
Faculty/School
School of Mathematics and Computer Science (SMCS)
Date of Award
Fall 2026
Advisor
Dr. Naveed Ahmad, Associate Professor, Department of Mathematical Sciences
Committee Member 1
Dr. Naveed Ahmad, Supervisor, Associate Professor, Department of Mathematical Sciences
Committee Member 2
Dr. MuhammadSarwar, External Examiner, University of Malakand, Chakdara
Committee Member 3
Dr. Abdul Majid, Program Director, Institute of Business Administration (IBA), Karachi
Project Type
Thesis
Access Type
Restricted Access
Document Version
Final
Pages
vii, 36
Keywords
Banach space, Hilbert space, Non-expansive mapping, variational inequality, fixed point, Self mapping, equilibrium problem
Abstract
In the thesis, we established the strong convergence of inertial iterative scheme designed to approximate the common solutions of the equilibrium and the fixed-point problem for non-expansive mappings in Hilbert spaces. Through extensive numerical analysis, we analyze the efficiency of the algorithm and demonstrate that the incorporation of the inertial technique yields a significantly faster convergence rate than existing comparable schemes. Furthermore, we examine the effect of initial value on the convergence dynamics, offering visual and comparative assessments against classical methods. To highlight the practical utility and versatility of our framework, we apply the algorithm to signal restoration problems, and we show that the proposed schemes extend naturally to variational inequality and constrained optimization problems.
Recommended Citation
Aijaz, F. (2026). Approximation of Solution of Certain Nonlinear Problems with Applications (Unpublished graduate thesis). Retrieved from https://ir.iba.edu.pk/etd-ms-math/8
FIXED POINT THEORY
