• 대한수학회논문집
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• 제31권3호
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.1-14
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• 2024

In this paper, we establish strong and ∆-convergence theorems for new iteration process namely S-R iteration process for a generalized α-nonexpansive mappings in a uniformly convex hyperbolic space and also we show that our iteration process is faster than other iteration processes appear in the current literature's. Our results extend the corresponding results of Ullah et al. [5], Imdad et al. [16] in the setting of uniformly convex hyperbolic spaces and many more in this direction.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.995-1009
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• 2021

Many iterative algorithms like that Picard, Mann, Ishikawa and S-iteration are very useful to elucidate the fixed point problems of a nonlinear operators in various topological spaces. The recent trend for elucidate the fixed point via inertial iterative algorithm, in which next iterative depends on more than one previous terms. The purpose of the paper is to establish convergence theorems of new inertial Picard normal S-iteration algorithm for nonexpansive mapping in Hilbert spaces. The comparison of convergence of InerNSP and InerPNSP is done with InerSP (introduced by Phon-on et al. [25]) and MSP (introduced by Suparatulatorn et al. [27]) via numerical example.

• East Asian mathematical journal
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• 제24권1호
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• pp.105-110
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• 2008

The aim of this paper is to prove convergence of implicit iteration process to a common fixed point for a finite family of strong successive $\Phi$-pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of S. S. Chang [On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 313(2006), 273-283], M. O. Osilike[Implicit iteration process for common fixed points of a finite finite family of strictly pseudocontractive maps, Appl. Math. Comput. 189(2) (2007), 1058-1065].

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.381-396
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• 2018

In this paper we have considered a system of mixed generalized variational inequality problems defined on two different domains in a Hilbert space. It has been shown that the solution of a system of mixed generalized variational inequality problems is equivalent to altering point formulation of some mappings. A new parallel S-iteration type process has been considered which converges strongly to the solution of a system of mixed generalized variational inequality problems.

• 한국인터넷방송통신학회논문지
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• 제12권4호
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• pp.119-130
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• 2012

최근 들어 소프트웨어 시스템은 점차적으로 복잡해지고 있으며, 고객(customer)은 보다 빠른 개발을 요구하고 있다. 전통적인(traditional) 순차적 접근법 (Sequential Approach)으로는 이러한 압력에 효과적으로 대처할 수 없어 대안으로 반복적 접근법 (Iterative Approach)이 적용되고 있다. 대표적인 반복적 접근법으로는 래쇼날의 단일화된 프로세스 (Rational Unified Process, RUP)가 있다. 그러나 RUP의 표준화된 수행방법은 단계, 반복과 활동들을 모두 순차적으로 수행하는 형태이다. 그 결과, 하나의 반복에서 수행된 하나의 활동은 다음 반복의 해당 활동이 수행될 때까지 기다려야 하는 인력낭비 현상이 발생한다. RUP를 수행하는 방법으로는 선형 접근법, 순차적 접근법, 중첩된 반복 접근법과 Time-boxed 반복 접근법이 제안되었다. 그러나 이들 방법은 인력낭비 현상 또는 적용시 프로젝트 관리의 어려움이라는 문제점을 갖고 있다. 본 논문은 활동들을 동시에 수행하는 방법을 제안하였다. 동시개발 접근법은 인력 낭비 현상을 방지할 수 있으며, 프로젝트 관리의 어려움도 해결할 수 있는 장점을 갖고 있다.

• East Asian mathematical journal
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• 제28권1호
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• pp.63-71
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• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.71-82
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• 2012

In this paper, we first show the weak convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings, which generalizes the result due to Khan and Fukhar-ud-din [1]. Next, we show the strong convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings satisfying Condition ($\mathbf{A}^{\prime}$), which generalizes the result due to Fukhar-ud-din and Khan [2].

• East Asian mathematical journal
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• 제28권1호
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• pp.81-92
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• 2012

The purpose of this paper is to establish strong convergence of an implicit iteration process to a common fixed point for a finite family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. Our results improve and extend the corresponding results of Fukhar-ud-din et al. [15] and some others from the current literature.