Article
Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings
Applied Mathematics and Computation (Impact Factor: 1.55). 03/2009; 209(2):162176. DOI: 10.1016/j.amc.2008.10.062
Source: DBLP
ABSTRACT
Let X be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. First purpose of this paper is to introduce a modified viscosity iterative process with perturbation for a continuous pseudocontractive selfmapping T and prove that this iterative process converges strongly to x∗∈F(T)≔{x∈X∣x=T(x)}, where x∗ is the unique solution in F(T) to the following variational inequality:〈f(x∗)x∗,j(vx∗)〉⩽0for allv∈F(T).Second aim of the paper is to propose two modified implicit iterative schemes with perturbation for a continuous pseudocontractive selfmapping T and prove that these iterative schemes strongly converge to the same point x∗∈F(T). Basically, we show that if the perturbation mapping is nonexpansive, then the convergence property of the iterative process holds. In this respect, the results presented here extend, improve and unify some very recent theorems in the literature, see [L.C. Zeng, J.C. Yao, Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings, Nonlinear Anal. 64 (2006) 2507–2515; H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279–291; Y.S. Song, R.D. Chen, Convergence theorems of iterative algorithms for continuous pseudocontractive mappings, Nonlinear Anal. (2006)].

 "for all í µí±¢, í µí±¢ † ∈ H. It is well known that, in a real Hilbert space H, the following equality holds: í®í´© í®í´© í®í´© í®í´© í®í´© í µí¼í µí±¢ + (1 − í µí¼) í µí±¢ † í®í´© í®í´© í®í´© í®í´© í®í´© 2 = í µí¼‖í µí±¢‖ 2 + (1 − í µí¼) í®í´© í®í´© í®í´© í®í´© í®í´© í µí±¢ † í®í´© í®í´© í®í´© í®í´© í®í´© 2 − í µí¼ (1 − í µí¼) í®í´© í®í´© í®í´© í®í´© í®í´© í µí±¢ − í µí±¢ † í®í´© í®í´© í®í´© í®í´© í®í´© 2 (10) for all í µí±¢, í µí±¢ † ∈ H and í µí¼ ∈ [0] [1]. "
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ABSTRACT: A hybrid iterative algorithm with MeirKeeler contraction is presented for solving the fixed point problem of the pseudocontractive mappings and the variational inequalities. Strong convergence analysis is given as . 
 "In a much more general setting, OsilikeUdomene [21], ZhangSu [33], ZhangGuo [32] and Zhou [37] investigated the weak convergence in a quniformly smooth Banach space. Since 1967, the construction of fixed points for pseudocontractions via the iterative process has been extensively investigated by many authors (see, e.g.,789 22]). In 1967, Halpern [15] introduced the following iteration which is the socalled Halpern iteration: x 1 ∈ C and "
Article: Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces
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ABSTRACT: We prove the strong convergence of the modified Manntype iterative scheme for a countable family of strict pseudocontractions in quniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y.H. Yao, H.Y. Zhou and Y.C. Liou, J. Appl. Math. Comput. 29, No. 1–2, 383–389 (2009; Zbl 1222.47129)]. 
Conference Paper: Characteristics of different power systems neutral groundingtechniques: facts and fiction
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ABSTRACT: The authors review the characteristics of different power systems grounding techniques as currently applied, and misapplied, within industry today. They note that, in many cases, misunderstood concepts and perceptions of the purpose and type of power systems grounding to be selected date back to the 1940s and earlier. Since that time much research, coupled with experience, that is now available to industry has taken place. The authors review the many different system grounding practices and present information on different grounding methods. Safety, National Electric Code requirements, and operational considerations, such as continuity of service, are investigated. Finally, examples of proper applications within various industries are given
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