In this paper, we introduce a new double inertial Mann-type iterative algorithm for approximating
a common solution of a demigeneralized fixed point problem and a monotone variational inequality
problem in reflexive Banach spaces. Our method is developed in the framework of Bregman distances
generated by a Legendre function, which provides a more general geometric structure than the classical
norm framework. Under suitable assumptions on the control parameters, the demigeneralized mapping,
and the monotone operator, we establish strong convergence of the proposed algorithm to a common
solution of the two problems. The results presented here extend and unify several existing schemes in
the literature, including classical Halpern iterations, inertial methods, and Bregman projection-type approaches.
In this paper, we introduce a novel two-step inertial Bregman--Tseng algorithm for solving non-monotone variational inequality problems in reflexive Banach spaces. The proposed method combines a two-step inertial extrapolation scheme with a Bregman forward-backward-forward (Tseng-type) framework, leading to a computati...
V. Darvish, Rehan Ali, Kobkoon Janngam· Journal of Advances in Optim...· 0 citations
In this paper, we introduce a novel two-step iterative algorithm based on a double inertial subgradient extragradient method for solving non-monotone variational inequality problems in reflexive Banach spaces. Without imposing any monotonicity conditions on the cost operator, we establish strong convergence of the prop...
G. Ugwunnadi, Jacob Ashiwere Abuchu, Abdul Rahim Khan et al.· Journal of Advances in Optim...· 0 citations
In this paper, we combine double inertial extrapolation with viscosity techniques to propose a novel iterative algorithm that finds a common solution to a generalized mixed equilibrium problem, a split variational inclusion problem, and a common fixed point constraint involving two nonexpansive operators in real Hilber...
A. Bnouhachem· Journal of Advances in Optim...· 0 citations
This paper proposes a two-step inertial Picard–CR iterative framework for approximating common fixed points of a countable family of nonexpansive mappings in real Hilbert spaces. The method combines a viscosity approximation with two inertial corrections and a Picard–CR-type fixed-point update. Under suitable control c...
A. E. Ofem, S. Moshokoa, M. Kekana et al.· International Journal of Ana...· 0 citations
This paper proposes an inertial Bregman subgradient extragradient algorithm for approximating a common solution of pseudomonotone equilibrium problems and fixed point problems associated with Bregman relatively nonexpansive mappings in reflexive Banach spaces. The proposed method incorporates an inertial extrapolation...
A. Kaewcharoen· International Journal of Ana...· 0 citations
