A strong convergence theorem for monotone inclusion and minimization problems in complete CAT(0) spaces

ABSTRACT

In this paper, a Halpern-type proximal point algorithm for approximating a common solution of monotone inclusion problem, minimization problem (MP) and fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a monotone inclusion problem, the set of solutions of an MP and the set of solutions of a fixed point problem for non-expansive mappings in complete CAT(0) spaces.

KEYWORDS:

• Monotone inclusion problem
• minimization problem
• fixed point problem
• monotone operators
• resolvent operators
• non-expansive mappings

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 47H10
• 49J20
• 49J40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF CoE-MaSS) Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.