نشریه علوم ریاضی و انفورماتیک

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Aremu K O, Izuchukwu C, Mewomo O T. Convergence Theorems for Proximal Point Method Involving Multivalued Nonexpansive Mappings in p-Uniformly Convex Metric Spaces. IJMSI 2025; 20 (2) :79-99
URL: http://ijmsi.ir/article-1-2105-fa.html

In this paper, we first extend the class of multivalued nonexpansive mappings to p-uniformly convex metric spaces. Furthermore, we propose and study an iterative algorithm involving p-resolvent operators of proper, convex and lowersemicontinuous functions for approximating a common solution of a finite family of minimization problems which is also a common fixed points of two multivalued nonexpansive mappings in p-uniformly convex metric space. Our proposed algorithm converges to a common element in the intersection of the set of minimizers of a finite family of proper, convex and lower semicontinuous functions and the set of common fixed points of two multivalued nonexpansive mappings. Finally, we demonstrate the applicability of our results with a numerical example. Our results improve many important and recent results in this direction.