Viscosity approximation method for split best proximity point and monotone variational inclusion problem

ABSTRACT

To address the split best proximity point and monotone variational inclusion problems in real Hilbert spaces, we present and investigate projection and viscosity approximation methods. Under a few reasonable assumptions, we prove some weak and strong convergence theorems for the aforementioned methods. The efficiency of the proposed method is demonstrated by some numerical examples. Some well-known recent results in this area have been improved, generalized, and extended as an outcome of this paper.

KEYWORDS:

• Best proximity point problem
• split variational inclusion problem
• strong convergence
• weak convergence
• viscosity approximation method

2010 AMS SUBJECT CLASSIFICATIONS:

• 41A29
• 47J25
• 49J40

Disclosure statement

No potential conflict of interest was reported by the author(s).