• 대한수학회논문집
• /
• 제31권4호
• /
• pp.845-855
• /
• 2016

We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

• 대한수학회논문집
• /
• 제31권3호
• /
• pp.575-583
• /
• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• East Asian mathematical journal
• /
• 제26권5호
• /
• pp.693-702
• /
• 2010

We study one-step iteration process to approximate common fixed points of two nonexpansive mappings and prove some convergence theorems in convex metric spaces. Using the so-called condition (A'), the convergence of iteratively defined sequences in a uniformly convex metric space is also obtained.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제22권2호
• /
• pp.185-197
• /
• 2015

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(f_n)-Lipschitzian map- pings and an infinite family of g_n-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

• Nonlinear Functional Analysis and Applications
• /
• 제27권3호
• /
• pp.621-640
• /
• 2022

The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.

• 대한수학회보
• /
• 제45권4호
• /
• pp.671-680
• /
• 2008

Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제29권4호
• /
• pp.335-352
• /
• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.