In this paper, some fixed point results of self mapping which is defined on Orthogonal cone metric spaces are given by using extensions of Orthogonal contractions. And by taking advantage of these results, the necessary conditions for self mappings on Orthogonal cone metric space to have P property are investigated. Also an example is given to illustrate the main results.

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In this research, performance analysis for the composition of non-Orthogonal and Orthogonal cellular digital television broadcasting is investigated. A downlink multi-carrier layered division multiplexing (LDM) superimposed with an evolved multimedia broadcast multicast service (eMBMS). We define two broadcast service providers (BSP), which offer different radio access technology (RAT). The BER and Sum-Rate efficiency are selected as our criteria. The proposed downlink composition framework can work without a subscriber identity module (SIM card) uplink and internet protocol (IP). Mathematical analysis, based on the exact closed-form expressions, is consistent with the theory of the proposed composition LDM/eMBMS. Evaluation and performance are done based on the Monte Carlo iterative methodology. The results show that the BER and Sum-Rate performance of a composition framework outperforms compared with LDM/eMBMS individually system.

In this paper we give a counter example for one of the lemmas of the paper” Frame of subspace in Wavelets, frames and operator theory” by P.G. Casazza and G. Kutyniok.

The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation nodes are positioned in the zeros of Orthogonal polynomials (Legendre, Lobatto, or Chebychev) or equally spaced nodal bases. A comparative study between the bases in the recovery of solutions to 1D and 2D elastostatic problems are performed. Examples are evaluated, and a significant improvement is observed when the SFEM, particularly the Lobatto approach, is used in comparison to the equidistant base interpolation.

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