• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.943-960
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• 2018

Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.

• East Asian mathematical journal
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• v.28 no.1
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• pp.63-71
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• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.43 no.6
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• pp.873-881
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• 2023

The evolution of civil engineering technology, exemplified by recent milestones like the completion of the Gangnam Global Business Center (GBC), has fostered the construction of expansive civil and architectural structures both above and below the earth's surface. This surge in construction necessitates a commensurate advancement in research and technology pertaining to safety protocols applicable to these vast edifices. Such protocols encompass a spectrum of concerns, ranging from the preemptive mitigation of accidents to the effective management of exigencies such as fires. As the trajectory of construction endeavors continues unabated, encompassing both subterranean and elevated domains, a concomitant imperative emerges to refine the methodologies underpinning precise indoor positioning. To address this need, an innovative web-based simulator has been devised to emulate indoor positioning scenarios for rigorous testing. This research further entails the development of an indoor positioning data Application Programming Interface (API) fortified by Geographic Information System (GIS) spatial operation techniques. This API is anchored in the construction of intricate test data, centered on the spatial layout of building 13 at the Electronics and Telecommunications Research Institute (ETRI). Consequently, the study renders feasible the expeditious provisioning of diverse signal-based and image-based spatial information, pivotal for enhancing the navigational acumen of mobile devices. Path delineation, cellular signal mapping, landmark identification, and ancillary navigational aids are among the manifold datasets promptly furnished by the indoor positioning data API. In summation, this study engenders a crucial leap towards the fortification of safety protocols and navigational precision within the expansive confines of modern architectural wonders.