The main purpose of this paper is to introduce and study a new class of generalized nonlinear setvalued quasi-variational inclusions system involving A, η -accretive mappings in Banach spaces. By using the resolvent operator due to Lan-Cho-Verma associated with A, η -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative a...

In the present work, chemotaxis-Naiver-Stokes system with rapidly decaying diffusivities \begin{document}$ \begin{eqnarray*} { \bf{(KSNS)} }\ \ \left\{ \begin{array}{llll} n_{t}+u\cdot\nabla n = \nabla\cdot(D(n)\nabla n)-\nabla\cdot(S(n)\nabla c), &&x\in\Omega, \, t>0, \\ c_{t}+u\cdot\nabla c \Delta - c+ n, u_{t}+\kappa(u\cdot\nabla)u u +\nabla P+ n\nabla\Phi, \nabla\cdot 0, t>0\ ...

Carbon dot (Cdot) nanoparticles are an emerging class of carbon nanomaterials with a promising potential for drug delivery and bio imaging applications. Although the interaction between Cdots and non-immune cell types has been well studied, Cdot interactions with macrophages have not been investigated. Exposure of Cdot nanoparticles to J774.1 cells, a murine macrophage cell line, resulted in mi...

The general potential of power-law inflation is as $ V(\phi)\propto \phi^{n} with scalar field $\phi$. behavior often known expansion like $S(\eta)\propto \eta^{1+\beta}$ $1+\beta<0$. In this paper, the theoretical spectra relic gravitational waves are compared measured strain sensitivity Advanced LIGO and VIRGO, corresponding to latest detected events waves. results show tight constraints on $...

Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u ∈ C such that 〈Au, J(v− u)〉 ≥ 0 for all v ∈ C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol’shteı̆n and Tret’yakov i...

The notion of accretive operator (see [1], [2]) plays an important part in the study of nonlinearsemigroups. According to this notion, we set up in the present study, essential properties of accretivity which allow to connect the set of linear accretive operators defined in a finite dimensional space with the set of M-matrix (see [3]). Such results allow us on one hand to make a link between va...

A new system of nonlinear fuzzy variational inclusions involving A, η -accretive mappings in uniformly smooth Banach spaces is introduced and studiedmany fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η -accretive operator due to Lan et al. and Nadler’s fixed points theorem for set-val...

Nigel Higson and John Roe Abstract: We connect the assembly map in C∗-algebra K-theory to rigidity properties for relative eta invariants that have been investigated by Mathai, Keswani, Weinberger and others. We give a new and conceptual proof of Keswani’s theorem that whenever the C∗-algebra assembly map is an isomorphism, the relative eta invariants associated to the signature operator are ho...

The purpose of this note is to prove an abstract operator version of certain existence theorems for differential and Volterra integral equations which deal with stability properties of solutions. We will do this in such a way that the results unify, as well as generalize, many of the basic theorems concerning stability of such equations. Thus, our main result(Theorem2)is an abstract version of ...