• The Mathematical Education
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• v.29 no.1
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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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• v.27 no.5
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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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• v.26 no.1
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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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• v.26 no.5
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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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• v.27 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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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].

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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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.

• Journal of the Korean Geotechnical Society
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• v.37 no.5
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• pp.5-17
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• 2021

In this study, the shear behavior between pile-sandy soil interface was quantified based on series of rigorous ring shear test results. Ring shearing test was carried out to observe the shear behavior prior to failure and behavior at residual state between most commonly used pile materials - steel and concrete - and Jumunjin sand. The test was set to clarify the shear behavior under various confinement conditions and soil densities. The test results were converted in to representative friction angles for various test materials. Additional numerical analysis was executed to validate the accuracy of the test results. Based on the test results and the numerical validation, it was found that due to the dilative and contractive nature of sand, its interface behavior can be categorized in to two different types : soils with higher densities tend to show peak shear stress and moves on to residual state, while on the other hand, soils with lower densities tend to show bilinear load-transfer curves along the interface. However, the relative density and the confining stress was found to affect the friction angle only in the small train range, and converges as it progresses to large deformation. This study established a large deformation analysis method which can successfully simulate and predict the large deformation behavior such as ring shear tests. Moreover, the friction angle derived from the ring shear test result and verified by numerical analysis can be applied to numerical analysis and actual design of various pile foundations.