In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems of the proposed iteration for an asymptotically nonexpansive nonself-mapping with the condition (BP). Finally, we give two examples to illustrate the main result in this paper. Our results...

Restriction Site Mapping is one of the interesting tasks in Computational Biology. A DNA strand can be thought of as a string on the letters A, T, C, and G. When a particular restriction enzyme is added to a DNA solution, the DNA is cut at particular restriction sites. The goal of the restriction site mapping is to determine the location of every site for a given enzyme. In partial digest metho...

This paper is concerned with the stabilization of nonholonomic systems in port-controlled Hamiltonian formulae via generalized canonical transformations. A special class of timevarying generalized canonical transformations are introduced which preserves the passivity property. Utilizing this transformation timevarying asymptotically stabilizing controllers for the nonholonomic Hamiltonian syste...

In the problem of selecting a linear model to approximate the true unknown regression model, some necessary and/or sufficient conditions are established for the asymptotic validity of various model selection procedures such as Akaike’s AIC, Mallows’ Cp, Shibata’s FPEλ, Schwarz’ BIC, generalized AIC, crossvalidation, and generalized cross-validation. It is found that these selection procedures c...

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotical...

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. ...

In this paper, we introduce and study a new class of generalized vector variational inequalities and complementarity problems for multivalued mappings. We prove the existence of solutions for this kind of vector variational inequality and discuss the relations between the solutions of the generalized vector variational inequalities and the solutions of generalized vector complementarity problem...

Additive models with backfitting algorithms are popular multivariate nonparametric fitting techniques. However, the inferences of the models have not been very well developed, due partially to the complexity of the backfitting estimators. There are few tools available to answer some important and frequently asked questions, such as whether a specific additive component is significant or admits ...

We extend a recent asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The maximum likelihood estimators of all model parameters have asymptotically normal distributions with mutual independence between fixed effects, covariance and parameters.