Оn a proximal point algorithm for solving minimization problem  and common fixed point problem in CAT($k$) spaces

C.  Garodia; S.  Radenovic

doi:10.37863/umzh.v75i2.6770

C. Garodia Jamia Millia Islamia, New Delhi, India
S. Radenovic University of Belgrade, Serbia

DOI: https://doi.org/10.37863/umzh.v75i2.6770

Keywords: Minimization problem; resolvent operator; CAT(1) space; proximal point algorithm; nonexpansive mapping.

Abstract

UDC 517.9

We propose a new modified proximal point algorithm in the setting of CAT(1) spaces, which can be used for solving the minimization problem and the common fixed-point problem. In addition, we prove several convergence results for the proposed algorithm under certain mild conditions. Further, we provide some applications for the convex minimization problem and the fixed point problem in the CAT($k$) spaces with a bounded positive real number $k$. In the process, several relevant results available in the existing literature are generalized and improved.

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