Abstract:
We introduce a general implicit iterative scheme base on viscosity approximation method with a ϕ-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator.

Abstract:
We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.

Abstract:
We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others.

Abstract:
We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others. 1. Introduction Throughout this paper we denoted by and the set of all positive integers and all positive real numbers, respectively. Let be a real Banach space, and let be a nonempty closed convex subset of . A mapping of into itself is said to be nonexpansive if for each . We denote by the set of fixed points of . We know that is nonempty if is bounded; for more detail see [1]. A one-parameter family from of into itself is said to be a nonexpansive semigroup on if it satisfies the following conditions: (i) ;(ii) for all ;(iii)for each the mapping is continuous;(iv) for all and . We denote by the set of all common fixed points of , that is, . We know that is nonempty if is bounded; see [2]. Recall that a self-mapping is a contraction if there exists a constant such that for each . As in [3], we use the notation to denote the collection of all contractions on , that is, . Note that each has a unique fixed point in . In the last ten years, the iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, for example, [3–5]. Let be a real Hilbert space, whose inner product and norm are denoted by and , respectively. Let be a strongly positive bounded linear operator on : that is, there is a constant with property A typical problem is to minimize a quadratic function over the set of the fixed points of a nonexpansive mapping on a real Hilbert space : where is the fixed point set of a nonexpansive mapping on and is a given point in . In 2003, Xu [3] proved that the sequence generated by converges strongly to the unique solution of the minimization problem (1.2) provided that the sequence satisfies certain conditions. Using the viscosity approximation method, Moudafi [6] introduced the iterative process for nonexpansive mappings (see [3, 7] for further developments in both Hilbert and Banach spaces) and proved that if is a real Hilbert space, the sequence generated by the following algorithm: where is a contraction mapping with constant and satisfies certain conditions, converges strongly to a fixed point of in which is unique solution of the variational inequality: In 2006, Marino and Xu [8] combined the iterative method (1.3)

Abstract:
We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given. 1. Introduction In the theory of variational inequalities and variational inclusions, the development of an efficient and implementable iterative algorithm is interesting and important. The important generalization of variational inequalities called variational inclusions, have been extensively studied and generalized in different directions to study a wide class of problems arising in optimization, nonlinear programming, finance, economics, and applied sciences. Variational inequalities are being used as a mathematical programming tool in modeling a wide class of problems arising in several branches of pure and applied mathematics. Several numerical techniques for solving variational inequalities and the related optimization problem have been considered by many authors. Throughout this paper, we denoted by and the set of all positive integers and all positive real numbers, respectively. Let be a real Banach space and be its dual space. Let denote the unit sphere of . is said to be uniformly convex if for each , there exists a constant such that for all , The norm on is said to be Gateaux differentiable if the limit exists for each , and in this case is smooth. Moreover, we say that the norm is said to have a uniformly Gateaux differentiable if the above limit is attained uniformly for all and in this case is said to be uniformly smooth. We define a function , called the modulus of smoothness of , as follows: It is know that is uniformly smooth if and only if . Let be a fixed real number . A Banach space is said to be -uniformly smooth if there exists a constant such that for all . From [1], we know the following property. Let be a real number with and let be a Banach space. Then, is -uniformly smooth if and only if there exists a constant such that The best constant in the above inequality is called the -uniformly smoothness constant of (see [1] for more details). Let be a real Banach space and the dual space of . Let denote the pairing between and .

Abstract:
Sensors based on the giant magnetoimpedance (GMI) effect in silicon steelswere constructed. Strips of silicon steels (0.500 mm-thick, 35.0 mm-long) with widthsranging from 0.122 to 1.064 mm were cut from recycled transformer cores. Since amaximum GMI ratio of 300% and a maximum field sensitivity of 1.5%/Oe were observedin a 1.064 mm-wide sample at 200 kHz, the 1.064 mm-wide strips were chosen as sensingelements in a slot key switch, angular velocity sensor, current sensor and force sensor. Thesensing elements were integrated into electronic circuits and the changes in impedancewere monitored. Variations in voltage due to these changes were typically small and musttherefore be amplified by the electronic circuits. For the current sensor and force sensor,the variation in the voltage drop across the GMI sensing element had non-linear variationswith either current or force and a conversion formula from a computer program wastherefore needed. The performance of the systems was tested. These sensing systems werestable, highly sensitive, hysteresis-free and could be produced on a mass scale. Based ontheir GMI effect, the silicon steels are versatile alternative low-cost sensors.

Abstract:
Cobalt of thickness from 1 to 25 mm was coated onto 120 mm-diameter silver wires by electrodeposition. Giant magneto-impedance (GMI) of electrodeposited cobalt on silver wires was measured with ac current from 1 kHz to 1 MHz. Their impedance decreased with a longitudinal magnetic field and saturated under 1.5 kOe. With increasing cobalt thickness, the critical frequency decreased but the GMI ratio increased. A maximum GMI ratio of over 200 % and sensitivity of about 0.5 %/Oe were observed in a 25 mm-thick sample at the frequency of about 500 kHz. The results can be explained by the dependence of the circumferential permeability on the magnetic field and frequency of ac current.

Giant magnetoimpedance effect (GMI) is a subject of special interest proved by applied electrodynamic and technological applications. GMI effect in ferromagnetic tubes is connected with the high sensitivity of the magnetic system to a circular magnetic field near the spin-reorientation magnetic phase transitions offering high sensitivity with respect to an external magnetic field. In this work the non-magnetic CuBe wires were covered by Fe_{20}Co_{6}Ni_{74} layers by electrodeposition. The thickness of 1 μm for magnetic layer was high enough in order to ensure the high GMI value. Longitudinal magnetic anisotropy was induced by post preparation annealing in a magnetic field of 160 A/m at 320℃ during 1 hour in order to obtain appropriate magnetisation process. Angular dependencies of GMI were measured in a frequency range of 1 to 10 MHz for driving currents of 2.5 to 20 mA. High longitudinal GMI of the order of 400% was observed at quite low frequency of 1 MHz. The highest value of the sensitivity of 520%/Oe was found for the active resistance: Linear sensitivities of 0.023 Ω/° and 0.05 Ω/° were observed for reasonably low fields of 240 and275 A/m respectively for small angles, where planar GMI elements are less effective.