• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.393-400
• /
• 2012

In this paper, we study the process of McShane delta integrals on time scales and discuss the relation between McShane delta integral and Henstock delta integral. We also prove the mono- tone convergence theorem, Fatou's Lemma and the dominated con- vergence theorems for the McShane delta integral.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.293-299
• /
• 2008

In this paper, we prove strong convergence theorems for a finite family of uniformly L-Lipschitzian mappings by a cyclic iterative algorithm in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.380-386
• /
• 1998

In this paper we introduce the concept of fuzzy integrals for set-valued mappings, which is an extension of fuzzy integrals for single-valued functions defined by Sugeno. And we give some properties including convergence theorems on fuzzy integrals for set-valued mappings.

• The Pure and Applied Mathematics
• /
• v.13 no.1 s.31
• /
• pp.39-46
• /
• 2006

We establish a general theorem to approximate fixed points of quasicontractive operators on a normed space through the Noor iteration process with errors in the sense of Liu [9]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1115-1126
• /
• 2020

The main purpose of this paper is to establish the rates of convergence in weak limit theorems for normalized geometric sums of independent identically distributed random variables via Zolotarev's probability metric.

• Korean Journal of Mathematics
• /
• v.23 no.3
• /
• pp.409-425
• /
• 2015

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.113-118
• /
• 1999

In this paper, we study the convergence theorem for the AP-integral based on the condition UAP and pointwise boundedness.

• Kyungpook Mathematical Journal
• /
• v.54 no.3
• /
• pp.375-385
• /
• 2014

We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces. Our results extend those announced by many authors.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.85-98
• /
• 2009

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].

• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.81-93
• /
• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.