in this note we point out and rectify some errors in a recently published paper “n. singh, r. jain: coupled fixed point results for weakly related mappings in partially ordered metric spaces, bull. iranian math. soc. 40 (2014), no. 1, 29-40”.

in the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎we also define the concept of weakly related mappings on an ordered space‎. ‎moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

We consider the supergravity dual descriptions of non-conformal super Yang-Mills theories realized on the world-volume of Dp-branes. We use the dual description to compute stress-energy tensor and current correlators. We apply the results to the study of dilatonic brane-worlds described by nonconformal field theories coupled to gravity. We find that brane-worlds based on D4 and D5 branes exhibi...

A parallel fully coupled one-level Newton-Krylov-Schwarz method is investigated for solving the nonlinear system of algebraic equations arising from the finite difference discretization of inverse elliptic problems. Both L and H least squares formulations are considered with the H regularization. We show numerically that the preconditioned iterative method is optimally scalable with respect to ...

The main part of this chapter is devoted to the development and presentation of a coupled multigrid method for the solution of saddle point systems (2.51) arising from the discretization of PDE constrained optimization problems. In subsequent chapters, the devised method will be adapted to handle inequality constraints on the control, and it will be employed for the solution of the systems, whi...

We present a scheme to simulate the coupled electron-ion dynamics within the density functional theory. In our scheme, letting the electrons and ions follow the time-dependent Kohn-Sham equation and the Newton equation, respectively, ultrafast dynamics induced by electronic excitation is investigated. We first show approximations made in that simulation to clarify the advantage and limitation o...