• East Asian mathematical journal
• /
• 제28권3호
• /
• pp.287-292
• /
• 2012

In this paper, we establish the strong convergence for the Mann iterative scheme associated with uniformly continuous pseudocontractive mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest.

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

• 호남수학학술지
• /
• 제39권1호
• /
• pp.1-25
• /
• 2017

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

• Korean Journal of Mathematics
• /
• 제18권3호
• /
• pp.299-309
• /
• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• East Asian mathematical journal
• /
• 제31권3호
• /
• pp.379-382
• /
• 2015

The purpose of this note is to study the estimation of errors of the implicit Mann iterative process with random errors.

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

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.763-771
• /
• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제11권4호
• /
• pp.337-348
• /
• 2004

In this paper, we suggest and analyze Noor (three-step) iterative scheme for solving nonlinear strongly accretive operator equation Tχ = f. The results obtained in this paper represent an extension as well as refinement of previous known results.

• 대한수학회논문집
• /
• 제30권3호
• /
• pp.209-219
• /
• 2015

In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

• 한국전자파학회논문지
• /
• 제28권10호
• /
• pp.819-824
• /
• 2017

본 논문은 distributed Multi-input Multi-output(MIMO) 레이다 시스템에서 다수의 송 수신기 조합으로부터 얻어진 Time of Arrival(ToA) 정보들을 이용하여 표적의 위치를 추정하는 기법을 제안한다. 제안된 기법은 테일러 선형 근사를 반복적으로 수행함으로써 임의의 초기 값으로부터 표적의 위치를 추정한다. 시뮬레이션 결과는 제안된 알고리즘이 기존 표적 위치 추정 기법들보다 더 향상된, 더 나아가 Cramer-Rao Lower Bound(CRLB)에 도달하는 평균제곱오차(MSE) 성능을 가지는 것을 보여준다.