• 한국수학교육학회지시리즈A:수학교육
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• 제29권1호
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• pp.41-45
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• 1990

S. Z. Wang, B. Y. Li, Z. M. Gao and K. Iseki proved some fixed point theorems on expansion mappings, which correspond some contractive mappings. In a recent paper, B. E. Rhoades generalized the results for in of mappings. In this paper, we obtain the following theorem, which generalizes the result of B. E. Rhoades. THEOREM. Let A, B, S and T be mappings from a complete metric space (X, d) into itself satisfying the following conditions: (1) ${\Phi}$(d(A$\chi$, By))$\geq$d(Sx, Ty) holds for all x and y in X, where ${\Phi}$ : R$\^$+/ \longrightarrowR$\^$+/ is non-decreasing, uppersemicontinuous and ${\Phi}$(t) < t for each t > 0, (2) A and B are surjective, (3) one of A, B, S and T is continuous, and (4) the pairs A, S and B, T are compatible. Then A, B, S and T have a unique common fixed point in X.

• East Asian mathematical journal
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• 제27권5호
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• pp.557-564
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• 2011

In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.117-135
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• 2021

Our purpose in this paper is to introduce the concept of complex valued convex metric spaces and introduce an analogue of the Picard-Ishikawa hybrid iterative scheme, recently proposed by Okeke [24] in this new setting. We approximate (common) fixed points of certain contractive conditions through these two new concepts and obtain several corollaries. We prove that the Picard-Ishikawa hybrid iterative scheme [24] converges faster than all of Mann, Ishikawa and Noor [23] iterative schemes in complex valued convex metric spaces. Also, we give some numerical examples to validate our results.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.917-933
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• 2021

In this paper, we investigate the behavior and sensitivity analysis of a solution set for a parametric generalized multi-valued nonlinear quasi-variational inclusion problem in a real Hilbert space. For this study, we utilize the technique of resolvent operator and the property of a fixed-point set of a multi-valued contractive mapping. We also examine Lipschitz continuity of the solution set with respect to the parameter under some appropriate conditions.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.757-771
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• 2022

In this paper, we present some fixed point theorems for rational type contractive conditions in the setting of a complete metric space via a cyclic (𝛼, 𝛽)-admissible mapping imbedded in simulation function. Our results extend and generalize some previous works from the existing literature. We also give some examples to illustrate the obtained results.

• 대한수학회논문집
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• 제39권1호
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• pp.149-160
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• 2024

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials A_Φ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|^-2 with a suitable domain generates a quasi-contractive, positive and analytic C₀-semigroup in L^p(ℝ^N , e^-Φ(x)dx), 1 < p < ∞. The proofs are based on an L^p-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].

• 대한수학회보
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• 제34권2호
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

• 한국지반공학회논문집
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• 제37권5호
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• pp.5-17
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• 2021

본 연구에서는 링전단시험 결과를 이용하여 말뚝-사질지반 사이의 전단거동을 정량화하였다. 링전단시험은 가장 일반적인 말뚝재료 - 콘크리트와 강 - 와 대표적인 사질토인 주문진표준사를 대상으로 수행하였으며, 두 재료 사이의 전단거동을 항복 이전과 잔류전단거동을 중심으로 확인하고 분석하였다. 시험결과를 통하여 다양한 상재압과 상대밀도의 영향 또한 분석하여, 그에 따른 전단거동을 각 재료 별 대표적인 마찰각으로 정량화하였다. 더 나아가, 추가적인 대변형 수치해석을 통하여 시험결과를 검증하였다. 링전단시험 및 수치해석을 수행한 결과, 사질토의 전단 중 발생하는 팽창과 수축특성에 의하여 전단거동을 크게 두 가지로 구분할 수 있었다. 1) 상대밀도가 높은 시료일수록 두 재료 간 전단응력곡선은 첨두전단응력이 관찰된 후 잔류전단응력이 발현되는 개형을 나타내었고, 반면에 2) 상대밀도가 낮은 시료일수록 두 재료 간 전단응력곡선은 첨두전단응력의 발현 없이 바로 잔류전단응력이 발현되는 이중곡선 형태를 보였다. 상재압은 소변형 범위에서는 전단거동 형태와 마찰각에 영향을 주지만, 상대밀도와 마찬가지로 대변형 하에서는 유의미한 영향을 주지 않는 것으로 확인되었다. 본 연구는 리메싱을 통한 대변형 수치해석 기법을 정립하여 링전단시험과 같은 대변형 전단거동을 모사하고 예측할 수 있도록 하였을 뿐 만 아니라, 링전단시험을 통하여 도출되고 대변형 수치해석으로 검증된 말뚝 재료와 사질토 사이의 마찰각은 실제 기초 말뚝의 수치해석과 설계에 적용할 수 있도록 하였다.