Search

The purpose of this paper is to study existence and approximation of solutions of system of variational inclusions involving multi-valued H-accretive and single-valued accretive operators over two different closed convex subsets of a Banach space. The convergence analysis of two proposed iteration processes for approximating solutions will be conducted within the conceptual framework of the ''altering point technique'' without uniform convexity of underlying spaces. This technique should make existing or new results in solving system of variational inequalities and variational inclusions. [ABSTRACT FROM AUTHOR]

We consider a new system of generalized variational inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space. To find the solution of considered SGVI, a parallel Mann iteration process and a parallel S-iteration process have been proposed and the strong convergence of the sequences generated by these parallel iteration processes is discussed. Numerical example illustrates that the proposed parallel S-iteration process has an advantage over parallel Mann iteration process in computing altering points of some mappings. [ABSTRACT FROM AUTHOR]

In this paper, by combining a modified extragradient scheme with the viscosity approximation technique, an iterative scheme is developed for computing the common element of the set of fixed points of a sequence of asymptotically nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse strongly monotone mapping. We prove a strong convergence theorem for the sequences generated by this scheme and give some applications of our convergence theorem. [ABSTRACT FROM AUTHOR]

It is well known that the rate of convergence of 5-iteration process introduced by Agarwal et al. [J. Nonlinear Convex Anal., 8 (1) (2007), 61-79.] is faster than Picard iteration process for contraction operators. Following the ideas of S-iteration process, we introduce a parallel S-iteration process for finding altering points of nonlinear operators. We apply our algorithms to solve a system of operator equations in Banach space setting. This work also includes convergence analysis of hybrid steepest-descent-like method and hybrid Newton-like method in the context of altering points. [ABSTRACT FROM AUTHOR]

Nanostructures are the building blocks of future nanodevices and thus methods for fabricating nanostructures of various materials in various forms are fundamentally important. Among those nanostructures ZnO has received much attention over the past few years due to the wide range of research by many different groups focused on different novel nanostructures with different properties. Although ZnO nanowires have been intensively studied, there are only a few methods that showed promising characteristics for practical applications. Without much effort, it can be grown in many different nanostructure forms, thus allowing various novel devices to be achieved. In this study, we intend to review those methods that enable nanostructure growth to be more controllable and feasible for applications. The methods for fabricating ZnO nanostructures are introduced in the first part. In the second part, the application of those nanostructures are mentioned and explained. Finally, the future realization of nanodevices is discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss some fundamental properties of Bregman distance, generalized projection operators, firmly nonexpansive mappings, and resolvent operators of set-valued monotone operators corresponding to a functional Φ(|| · ||). We further study some proximal point algorithms for finding zeros of monotone operators and solving generalized mixed equilibrium problems in Banach spaces. Our results improve and extend some recent results concerning generalized projection operators corresponding to Bregman distance. [ABSTRACT FROM AUTHOR]

Let X be a real reflexive Banach space with a weakly continuous duality mapping Jφ. Let C be a nonemptyweakly closed star-shaped (with respect to u) subset of X. Let F= {T(t) : t ∊ [0, + ∞)} be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of C, which is uniformly continuous at zero. We will showthat the implicit iteration scheme: yn = αnu+(1-αn)T(tn)yn, for all n ∊ N, converges strongly to a common fixed point of the semigroup F for some suitably chosen parameters {αn} and {tn}. Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009). [ABSTRACT FROM AUTHOR]

We introduce an explicit iterative scheme for computing a common fixed point of a sequence of nearly nonexpansive mappings defined on a closed convex subset of a real Hilbert space which is also a solution of a variational inequality problem. We prove a strong convergence theorem for a sequence generated by the considered iterative scheme under suitable conditions. Our strong convergence theorem extends and improves several corresponding results in the context of nearly nonexpansive mappings. [ABSTRACT FROM AUTHOR]

The hybrid steepest-descent method introduced by Yamada (2001) is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and applicable to a broad range of convexly constrained nonlinear inverse problems in real Hilbert spaces. Lehdili and Moudafi (1996) introduced the new prox-Tikhonov regularization method for proximal point algorithm to generate a strongly convergent sequence and established a convergence property for it by using the technique of variational distance in Hilbert spaces. In this paper, motivated by Yamada's hybrid steepest-descent and Lehdili and Moudafi's algorithms, a generalized hybrid steepest-descent algorithm for computing the solutions of the variational inequality problem over the common fixed point set of sequence of nonexpansive-type mappings in the framework of Banach space is proposed. The strong convergence for the proposed algorithm to the solution is guaranteed under some assumptions. Our strong convergence theorems extend and improve certain corresponding results in the recent literature. [ABSTRACT FROM AUTHOR]

Al2O3–ZrO2 composites were sintered using low cost extended arc thermal plasma reactor and conventional heating. Composites prepared in a wide range of composition were studied in terms of their density, shrinkage, hardness, structure, microstructure and dielectric response. Experimental parameter such as sintering time, sintering temperature and plasma power were optimized to achieve higher sintered end product. Highly dense sintered products were obtained by plasma heating route within short sintering time compared with conventional sintered method. Interesting development pertaining to structure and phase evolution, structure and dielectric response are analyzed. It is found that compositional variation in this composite produces structural phase separation at different sintering conditions, which is more in plasma heating product than conventional heated product. Plasma sintered product always shows less dielectric constant as compared to conventional sintered sample. [ABSTRACT FROM AUTHOR]

In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature. [ABSTRACT FROM AUTHOR]

Polycrystalline Zn1-x(Mn:Ni)x0 sample for x = 0.02 were synthesized by solid state route. We have observed low field microwave absorption in these powder samples. Low field microwave absorption signal is out of phase with the regular resonance signal indicating the microwave absorption has a minimum at zero field and the absorption of microwaves increases with increase of magnetic field. Low field microwave absorption in these powders is qualitatively different from their bulk pellets. Temperature dependence of the low field microwave absorption indicates a line shape evolution and a non-monotonic peak to peak intensity change. Further, we have observed the absence of 2nd harmonic in this low field microwave absorption, indicating low field microwave absorption in these transition metal co-doped ZnO powders is not non-linear in nature. [ABSTRACT FROM AUTHOR]