Viscosity approximation methods for W-mappings in Hilbert space

Subject Areas : Applied Mathematics

HR  Sahebi ¹ (Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.)
S.  Ebrahimi ² (Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.)

Received: 2016-06-07 Accepted : 2016-12-20 Published : 2017-12-01

Keywords: fixed point, Nonexpansive mapping, equilibrium problems, Hilbert space, W-mapping, strongly positive linear bounded operator,

Abstract :

We suggest a explicit viscosity iterative algorithm for nding a common elementof the set of common xed points for W-mappings which solves somevariational inequality. Also, we prove a strong convergence theorem with somecontrol conditions. Finally, we apply our results to solve the equilibrium problems.Finally, examples and numerical results are also given.