A modified proximal point algorithm in geodesic metric space

Abstract

<abstract><p>Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove $ \Delta $ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.</p></abstract>

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

“…The classical Banach contraction theorem [1] is an important and fruitful tool in nonlinear analysis. In the past few decades, many authors have extended and generalized the Banach contraction mapping principle in several ways (see [2][3][4][5][6][7][8][9][10][11][12]). On the other hand, several authors, such as Boyd and Wong [13], Browder [14], Wardowski [15], Jleli and Samet [16], and many other researchers have extended the Banach contraction principle by employing different types of control functions (see [17][18][19][20][21] and the references therein).…”