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Convergence Theorems of an Implicit Iterates with Errors for Non-Lipschitzian Asymptotically Quasi-Nonexpansive Type Mappings
G. S. Saluja
International Journal of Analysis and Applications , 2013,
Abstract: The aim of this paper is to study an implicit iterative process with errors for two finite families of non-Lipschitzian asymptotically quasi-nonexpansive type mappings in the framework of real Banach spaces. In this paper, we have obtained a necessary and sufficient condition to converge to common fixed points for proposed scheme and mappings and also obtained strong convergence theorems by using semi-compactness and Condition (B’).
An implicit iterative algorithm with errors for two families of generalized asymptotically nonexpansive mappings  [cached]
Agarwal Ravi,Qin Xiaolong,Kang Shin
Fixed Point Theory and Applications , 2011,
Abstract: In this paper, an implicit iterative algorithm with errors is considered for two families of generalized asymptotically nonexpansive mappings. Strong and weak convergence theorems of common fixed points are established based on the implicit iterative algorithm. Mathematics Subject Classification (2000) 47H09 · 47H10 · 47J25
Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces
Hafiz Fukhar-Ud-Din,Abdul Rahim Khan
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.1643
Abstract: We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappings is unbounded, (ii) the iterative sequence contains an error term.
CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
Gu Feng,
谷峰

数学物理学报(A辑) , 2006,
Abstract: The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve thecorresponding results of 1, 2, 4-9, 11-15].
Convergence of Common Random Fixed Point of Finite Family of Asymptotically Quasi-Nonexpansive-Type Mappings by an Implicit Random Iterative Scheme  [PDF]
A. S. Saluja,Pankaj kumar Jhade
Journal of Mathematics , 2013, DOI: 10.1155/2013/678946
Abstract: We introduce a new implicit random iteration process generated by a finite family of asymptotically quasi-nonexpansive-type mappings and study necessary and sufficient conditions for the convergence of this process in a uniformly convex Banach space. The results presented in this paper extend and improve the recent ones announced by Plubtieng et al. (2007), Beg and Thakur (2009), and Saluja and Nashine (2012). 1. Introduction Probabilistic functional analysis has come out as one of the momentous mathematical disciplines in view of its requirements in dealing with probabilistic models in applied problems. The study of random fixed points forms a central topic in this area. Random fixed point theorems for random contraction mappings on separable complete metric spaces were first proven by ?pa?ek [1]. Subsequently, Bharucha-Reid [2] has given sufficient conditions for a stochastic analog of Schauder’s fixed point theorem for a random operator. The study of random fixed point theorems was initiated by ?pa?ek [1] and Han? [3, 4]. In an attempt to construct iterations for finding fixed points of random operators defined on linear spaces, random Ishikawa scheme was introduced in [5]. This iteration and also some other random iterations based on the same ideas have been applied for finding solutions of random operator equations and fixed points of random operators (see [5]). Recently, Beg [6], Choudhury [7], Duan and Li [8], Li and Duan [9], Itoh [10], and many others have studied the fixed point of random operators. Beg and Abbas [11] studied the different random iterative algorithms for weakly contractive and asymptotically nonexpansive random operators on arbitrary Banach spaces. They also established the convergence of an implicit random iterative process to a common random fixed point for a finite family of asymptotically quasi-nonexpansive operators. In 2007, Plubtieng et al. [12] studied the implicit random iteration process with errors, which converges strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive random operators on an unbounded set in uniformly convex Banach spaces and proves some strong convergence theorems. An implicit process is generally desirable when no explicit scheme is available. Such a process is generally used as a “tool” to establish the convergence of an explicit scheme. Recently, Beg and Thakur [13] introduced modified general composite implicit random iteration process and proved some strong convergence theorems for a finite family of random asymptotically nonexpansive mappings in separable
Weak and strong convergence of an implicit iterative process with errors for a finite family of asymptotically quasi $I-$nonexpansive mappings in Banach space  [PDF]
Farrukh Mukhamedov,Mansoor Saburov
Mathematics , 2010,
Abstract: In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\{T_j\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of $\{I_j\}_{j=1}^N$ of asymptotically quasi nonexpansive mappings in the framework of Banach spaces.
Fixed point theorems for generalized weakly contractive mappings
Ramendra Krishna Bose,Mrinal Kanti Roychowdhury
Surveys in Mathematics and its Applications , 2009,
Abstract: In this paper several fixed point theorems for generalized weakly contractive mappings in a metric space setting are proved. The set of generalized weakly contractive mappings considered in this paper contains the family of weakly contractive mappings as a proper subset. Fixed point theorems for single and multi-valued mappings, approximating scheme for common fixed point for some mappings, and fixed point theorems for fuzzy mappings are presented. It extends the work of several authors including Bose and Roychowdhury.
Convergence of Ishikawa iterates of generalized nonexpansive mappings  [cached]
M. K. Ghosh,L. Debnath
International Journal of Mathematics and Mathematical Sciences , 1997, DOI: 10.1155/s0161171297000707
Abstract: This paper is concerned with the convergence of Ishikawa iterates of generalized nonexpansive mappings in both uniformly convex and strictly convex Banach spaces. Several fixed point theorems are discussed.
Strong convergence of an implicit iteration process for a finite family of strictly asymptotically pseudocontractive mappings
Singh Saluja,Gurucharan; Kumar Nashine,Hemant;
Cubo (Temuco) , 2011, DOI: 10.4067/S0719-06462011000100009
Abstract: in this paper, we establish the strong convergence theorems for a finite family of kstrictly asymptotically pseudo-contractive mappings in the framework of hilbert spaces. our results improve and extend the corresponding results of liu [5] and many others.
On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense
Xiaolong Qin,Jong Kyu Kim,Tianze Wang
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/468716
Abstract: An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.
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