A new class of inertial algorithms with monotonic step sizes for solving fixed point and variational inequalities

Abstract

This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for 𝜌-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.

Single-Valued Demicontractive Mappings: Half a Century of Developments and Future Prospects

“…For other important recent results regarding the study of VIP over the set of fixed points of demicontractive mappings and of finite families of demicontractive mappings, we refer to Maingé [22,103], Suantai and Phuengrattana [2], Thong and Hieu [104], Ogbuisi and Mewomo [105], Alakoya et al [106], Meddahi et al [107], Linh et al [108], Okeke et al [109,110], Rehman et al [111], Sow [112][113][114], Tan et al [115,116], Thong et al [117,118], Thong and Hieu [104,119], Amarachi Uzor et al [120], etc.…”