Approximate solution of zero point problem involving H-accretive maps in Banach spaces and applications

• Main Authors: Rajat Vaish, Mohd. Sarfaraz, Md. Kalimuddin Ahmad, Kaleem Raza Kazmi
• Format: Article
• Language: English
• Published: SpringerOpen 2019-07-01
• Series: Journal of Inequalities and Applications
• Subjects: H-accretive mappings; Alternating resolvents; Mann’s iteration; Halpern iteration; Viscosity approximation method; Banach space
• Online Access: http://link.springer.com/article/10.1186/s13660-019-2163-y
• ISSN: 1029-242X

Abstract In this manuscript, we introduce two iterative methods for finding the common zeros of two H-accretive mappings in uniformly smooth and uniformly convex Banach spaces. The proposed iterative methods are based on Mann and Halpern iterative methods and viscosity approximation method. Strong convergence results are established for iterative algorithms. Applications based on convex minimization problem, variational inequality problem and equilibrium problem are derived from the main result. Numerical implementation of the main results and application are demonstrated by some examples. Our results extend, generalize, and unify the previously known results given in literature.