Abstract: The Jacobi polynomial P_n⁽α^,β⁾(x) which is obtained from Jacobi differential equation is an orthogonal polynomial over the interval [-1, 1] with respect to weight function _(1-x)α_(1+x)β, α>-1, β>-1. Here Jacobi series has been taken and established a theorem on lower triangular matrix summability of a Jacobi series.

Abstract: In this paper, we obtain a common fixed point theorem by employing the notion of g-reciprocal continuity in symmetric spaces. We demonstrate that g-reciprocal continuity ensures the existence of common fixed point under strict contractive conditions, which otherwise do not ensure the existence of fixed points.

Abstract: In this paper, the author has established Hermite- Hadamard’s inequalities for preinvex functions and has extended some estimates of the right side of a Hermite- Hadamard type inequalities for preinvex functions via fractional integrals.

Abstract: In the present paper, we construct the traveling wave solutions involving parameters of some nonlinear PDEs in mathematical physics via the nonlinear SchrÖdinger (NLS−) equation and the regularized long-wave (RLW) equation by using a simple method which is called the (G’/G) -expansion method, where G=G(ζ) satisfies the second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear PDEs arising in mathematical physics.