• Journal of the Korean Geotechnical Society
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• v.19 no.5
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• pp.199-210
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• 2003

The development of strain localization within shear zones is frequently observed during soil deformation. In fact, the phenomenon appears to be more often the norm rather than the exception. Conceptually, any soil condition that renders negative work increment is prone to localization. In this study, a broad range of soil and loading conditions are investigated to test this criterion, including: dilative soil subjected to drained shear (standard case), contractive soil sheared under undrained conditions, cavitation in dilative soil in undrained shear, inhomogeneous soils, particle alignment in contractive soils made of platy particles, soils that experience particle crushing, and the shear of low-moisture and/or lightly cemented loose soils. Unique specimens and test procedures are designed to separately test each of these soil conditions in the laboratory According to experimental test results, soil specimens with post-peak strain softening behavior are prone to progressive failure, localization of deformations, and shear banding. The state of stress, the soil density, inherent mechanical and geometrical properties of soil particles, low water content, and heterogeneity can contribute to triggering strain localization. Considering all possible cases of localization, the best method to obtain the critical state line in the laboratory is to use contractive homogeneous specimens subjected to drained shear.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.157-165
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• 2014

In this paper, we obtain some common fixed point theorems of single and multivalued maps under hybrid contractive conditions satisfying weakly commuting in IFMS. Our results extend previous ones in IFMS.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.121-129
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• 2010

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

• East Asian mathematical journal
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• v.37 no.1
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• pp.123-130
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• 2021

In this paper, we introduce the new concept of a cone metric-like space and consider some fixed point theorems for generalized contractive mappings under suitable conditions in cone metric-like spaces. Our results generalize and unify the several main results of [1, 2, 9].

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1003-1021
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• 2015

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.149-160
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• 2018

In this paper, we prove a strong convergence result under an iterative scheme for N finite asymptotically $k_i-strictly$ pseudo-contractive mappings and a firmly nonexpansive mappings $S_r$. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the corresponding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.45-60
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• 2023

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.559-580
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• 2024

In this paper, we aim to prove coupled and common coupled fixed point theorems for contractive type conditions in the context of partial metric spaces by means of a control function, and to provide some corollaries of the established results. This paper presents a number of results that generalize and extend previous work in the field. In order to better illustrate the process, we provide examples.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.537-545
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• 2007

Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in the setup of certain metrizable topological vector spaces are obtained. As applications, related results on best approximation are derived. Our results extend, generalize and unify various known results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.671-680
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• 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.