In this work, we consider the problem of magneto-thermoelastic interactions in a functionally graded material (FGM) under dual-phase-lag model in the presence of thermal shock. The generalized thermoelasticity theory with one relaxation time has been employed. The material is assumed to be elastic and functionally graded (FGM) (i.e. material with spatially varying properties). The basic equations have been written in the form of a vectormatrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Stehfest method. Further, graphs have been drawn to show the effect of the nonhomogeneity parameter, magnetic field, and dual-phase-lag parameters on displacement, temperature, stress, and strain.

We have defined the variable exponent of the Cesàro complex function space of formal power series. We have constructed the prequasi-ideal generated by s -numbers and this new space of complex functions. We present some topological and geometric structures of this class of ideal. The existence of Caristi’s fixed point is examined. Some geometric properties related to the fixed point theory are presented. Finally, real-world examples and applications show solutions to some nonlinear difference equations.

In the present paper we introduced the ideal convergence of generalized difference sequence spaces combining de La Vallée-Poussin mean and Musielak-Orlicz function overn-normed spaces. We also study some topological properties and inclusion relation between these spaces.