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In this article, an Ishikawa iteration scheme is modified for b$$ b $$‐enriched nonexpansive mapping to solve a fixed point problem and a split variational inclusion problem in real Hilbert spaces. Under some suitable conditions, we obtain convergence theorem. Moreover, to demonstrate the effectiveness and performance of proposed scheme, we apply the scheme to solve a split feasibility problem and compare it with some existing iterative schemes. [ABSTRACT FROM AUTHOR]

This paper provides iterative construction of a common solution associated with the fixed point problem of an infinite family of |-demicontractive mappings, pseudomonotone equilibrium problem satisfying Lipschitz-type continuity and the split common null point problem. We propose an iterative algorithm that combines the classical extragradient method with the inertial extrapolation technique. The analysis of the proposed algorithm is two-fold: firstly, we establish strong convergence results under suitable set of constraints and secondly we verify the viability of the proposed algorithm via numerical experiment with applications. [ABSTRACT FROM AUTHOR]

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications. [ABSTRACT FROM AUTHOR]

An inertial Mann algorithm will be presented in this article with the purpose of approximating a fixed point of a nonexpansive mapping on a Hadamard manifold. Any sequence that is generated by using the proposed approach, under suitable assumptions, converges to fixed points of nonexpansive mappings. The proposed method is also dedicated to solving inclusion and equilibrium problems. Lastly, we give a number of computational experiments that show how well the inertial Mann algorithm works and how it compares to other methods. [ABSTRACT FROM AUTHOR]

This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ρ$$ \rho $$‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings. [ABSTRACT FROM AUTHOR]

This paper provides iterative solutions, via some variants of the extragradient approximants, associated with the pseudomonotone equilibrium problem (EP) and the fixed point problem (FPP) for a finite family of η-demimetric operators in Hilbert spaces. The classical extragradient algorithm is embedded with the inertial extrapolation technique, the parallel hybrid projection technique and the Halpern iterative methods for the variants. The analysis of the approximants is performed under suitable set of constraints and supported with an appropriate numerical experiment for the viability of the approximants. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and consider a new generalized system of nonlinear mixed variational inequality involving three difference relaxed cocoercive operators. This work is to use the resolvent operator technique to find the common solutions for a new generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for an -inverse-strongly-monotone mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a monotone mapping. [Copyright &y& Elsevier]

In this paper, we introduce an iterative scheme with inertial effect using Mann iterative scheme and gradient-projection for solving the bilevel variational inequality problem over the intersection of the set of common fixed points of a finite number of nonexpansive mappings and the set of solution points of the constrained optimization problem. Under some mild conditions we obtain strong convergence of the proposed algorithm. Two examples of the proposed bilevel variational inequality problem are also shown through numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we present a new iterative algorithm for finding a common element of three solution sets; (i) split equilibrium problem; (ii) general system of finite variational inequality problem; and (iii) fixed point problem. This algorithm is modified by hybrid method based on Cesàro mean in real Hilbert spaces. Furthermore, a strong convergent theorem is established and this theorem is the generalization of many previously known results in this research area. Finally, we study the rate of convergence of the iterative algorithm and some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]