• 대한수학회지
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• 제34권1호
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• pp.237-245
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• 1997

The fixed point index plays an important role in solving the positive solutions of nonlinear equations in ordered Banach spaces ([7], [10], [11], [14], [15]). Many authors have studied the existence problems of positive solutions of nonlinear equations for nonlinear mappings ([1]-[5], [7], [9], [10], [14], [15]).

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.785-795
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• 2022

In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.69-88
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• 2022

In this work, the three-step intermixed iteration for two finite families of nonlinear mappings is introduced. We prove a strong convergence theorem for approximating a common fixed point of a strict pseudo-contraction and strictly pseudononspreading mapping in a Hilbert space. Some additional results are obtained. Finally, a numerical example in a space of real numbers is also given and illustrated.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.309-322
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• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• 전자공학회논문지
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• 제50권6호
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• pp.3-8
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• 2013

비트 패턴 미디어 (BPM) 저장장치는 기존 자기 기록장치의 한계를 극복하기 위한 기술 중 하나로 주목 받고 있다. 하지만 고밀도의 BPM 저장창치에서는 트랙간의 간섭 (ITI), 심벌간의 간섭 (ISI), 잡음이 비트 오율 (BER)을 심각하게 저하시키는 문제가 있다. 본 논문에서는 ITI와 ISI의 악영향을 경감시키기 위해 축약사상 기반의 단순 반복적 2차원 등화기를 제안한다. 또한 제안한 2차원 등화기에 대한 BPM 저장장치의 채널 특성이 수렴 조건을 만족함을 살펴보았다. 모의실험에서 1차원 등화기와 2차원 등화기의 비트 분리 특성 차이를 보였고, 제안한 등화기의 BER 성능을 다른 등화 방법과 비교하여 평가하였다. 실험결과에 의하면 본 논문에서 제안한 등화기는 적당한 복잡도를 유지하면서 고밀도 BPM 저장장치를 위한 훌륭한 등화기라 할 수 있다.

• 대한수학회보
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• 제50권3호
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• pp.1007-1020
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• 2013

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.

• 충청수학회지
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• 제3권1호
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• pp.103-110
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• 1990

Let K be a nonempty weakly compact convex subset of a Banach space X and T : K ${\rightarrow}$ C(X) a nonexpansive mapping satisfying $P_T(x){\cap}clI_K(x){\neq}{\emptyset}$. We first show that if I - T is semiconvex type then T has a fixed point. Also we obtain the same result without the condition that I - T is semiconvex type in a Banach space satisfying Opial's condition. Lastly we extend the result of [5] to the case, that T is an 1-set contraction mapping.

• 충청수학회지
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• 제33권4호
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• pp.387-394
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• 2020

Matthews introduced the concepts of partial metric spaces and proved the Banach fixed point theorem in complete partial metric spaces. Dukic, Kadelburg, and Radenovic proved fixed point theorems for Geraghty-type mappings in complete partial metric spaces. In this paper, we prove the fixed point theorem for some contractive mapping in a complete partial metric space.

• 대한수학회지
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• 제42권2호
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• pp.255-268
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• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• 대한수학회논문집
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• 제34권4호
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• pp.1201-1222
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• 2019

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.