In this paper, we consider and analyze a new class of extragradient-type methods for solving general variational inequalities. The modified methods converge for pseudomonotone operators which is weaker condition than monotonicity. Our proof of convergence is very simple as compared with other methods. The proposed methods include several new and known methods as special cases. Our results prese...

The purpose of this work to investigate pseudomonotone and Lipschitz continuous variational inequalities in real Hilbert spaces. For solving problem, we propose two new methods which combine advantages the subgradient extragradient method projection contraction method. Similar some recent developments, proposed do not require knowledge constant associated with inequality mapping. Under suitable...

Abstract In this paper, we study the problem of finding a common solution pseudomonotone variational inequality and fixed point for demicontractive mappings. We introduce new inertial iterative scheme that combines Tseng’s extragradient method with viscosity together adaptive step size technique investigated problem. prove strong convergence result our proposed algorithm under mild conditions w...

<p style='text-indent:20px;'>In this paper, we propose a new inertial Tseng's extragradient iterative algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz operator in real Hilbert spaces. We prove that the sequence generated by proposed converges strongly to an element solutions problem under some suitable assumptions imposed on parameters. Finally, g...