• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.411-432
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• 2021

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.841-865
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• 2024

In this research, we propose a new efficient iterative method for fixed point problems of generalized α-nonexpansive mappings. We show the weak and strong convergence analysis of the proposed method under some mild assumptions on the control parameters. We consider the application of the new method to some real world problems such as convex minimization problems, image restoration problems and impulsive fractional differential equations. We carryout a numerical experiment to show the computational advantage of our method over some well known existing methods.