In this work, we prove the strong convergence of an inertial iterative scheme to approximate solutions of the equilibrium fixed point problem associated with nonexpansive mappings in Hilbert spaces. Numerical simulations are carried out to examine the performance of the proposed approach. The results indicate that the proposed inertial approach achieves faster convergence when compared with existing comparable iterative schemes. We also investigate how different choices of initial values influence the convergence behavior of our algorithms and we compare these effects with those observed in classical iterative schemes through graphical illustrations. In applications, we used our approach to solve the signal processing problem. We also apply it to a mathematical model describing the spread of an infectious disease, which illustrates its relevance to real-world dynamical systems. Finally, we show that the proposed method can be applied in solving constrained optimization, variational inequality and split feasibility problems which highlight its flexibility and wide applicability.
This paper introduces a dynamic simultaneous iterative scheme for solving split equality
monotone variational inclusion problems in real Hilbert spaces, where the associated operators are assumed
to be firmly quasi-non expan-sive. Under appropriate conditions on the parameters, we prove that
the generated sequence conv...
Mohd Asad, Mubashshir U. Khairoowala, S. Husain· Optimization Eruditorum· 0 citations
This study focuses on a three-step iterative scheme, referred to as the NIP iteration, for the approximation of fixed points associated with nonexpansive mappings in uniformly convex Banach spaces. Weak convergence is established using Fejér monotonicity, asymptotic regularity and the demiclosedness principle. Strong c...
F. Alamrani, Nidal H. E. Eljaneid, N. Altaweel et al.· Axioms· 0 citations
This work presents the study of Adaptive variational iteration method (AVIM), an enhanced semi-analytical technique for solving nonlinear partial differential equations (PDEs). The AVIM is a modification of the classical variational iteration method (VIM), in which an adaptive Lagrange multiplier is dynamically updated...
A. M. Umar, K. Oduwole, G. S. Esomnofu· Fulafia Journal of Science a...· 0 citations
We study two-point fractional boundary value problems with uncertain input data, where randomness may enter through the coefficients and boundary conditions. To quantify the resulting uncertainty in the solution, we employ the generalized polynomial chaos (gPC) framework and develop a stochastic Galerkin formulation of...
In this paper, we propose a resolvent-free and projection-free iterative algorithm to solve monotone inclusion problems. The proposed method employs a double inertial extrapolation strategy, in which two distinct inertial steps are used to construct two extrapolated points, together with a new self-adaptive step-size f...
Mujahid Abbas, Muhammad Waseem Asghar· Computation· 0 citations
We study a nonlinear Dirichlet boundary value problem with the variable exponent p(x)-Laplacian and a reaction term. First, we prove the existence and uniqueness of a weak solution by minimizing the associated energy functional. To deal with possible singularities in the operator, we introduce a relaxed energy through...
