Abstract
In this paper, we prove some Δ-convergence and strong convergence results for the sequence generated by a new algorithm to a minimizer of two convex functions and a common fixed point for quasi-pseudo-contractive mappings in Hadamard spaces. Our theorems improve and generalize some recent results in the literature.
Highlights
Let ( X,d ) be a metric space and x, y ∈ X with l = d ( x, y)
A metric space X is a geodesic space if every two points of X are joined by a geodesic segment
A geodesic triangle ∆ ( x1, x2, x3 ) in a geodesic space X consists of three points x1, x2, x3 of
Summary
In 2015, Cholamjiak-Abdou-Cho [13] established strong convergence of the sequence to a minimizer of a convex function and to a fixed point of nonexpansive mappings in CAT(0) spaces. In 2019, Chang et al [14] presented a new modified proximal point algorithm for solving the minimization of a convex function and the common fixed points problem for two k-strictly pseudononspreading mappings in Hadamard spaces. It is easy to see that the class of quasi-pseudo-contractive mappings is fundamental It includes many kinds of nonlinear mappings such as the demicontractive mappings, the quasi-nonexpansive mappings and the k-strictly pseudononspreading with fixed points as special cases. Motivated by the researches above, we establish the convergent results to a minimizer of two convex functions and a common fixed point of quasi-pseudo-contractive mappings in Hadamard spaces. Our results generalize the corresponding results of Cholamjiak-Abdou-Cho [13], Chang et al [14], Ariza-Ruiz et al [15], Bačák [16], Dhompongsa et al [17], Khan-Abbas [18] and many others
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