A New Approach for the Solution of the Electrostatic Potential Differential Equations

This paper is focused on deriving an explicit analytical solution for the prediction of the electrostatic potential, commonly used on electrokinetic research and its related applications. Different from all other analytic techniques, this approach provides a simple way to ensure the convergence of series of solution so that one can always get accurate enough approximations. This new approach can be a useful tool in electrical field applications such as the separation of a mixture of macromolecules and the removal of contaminants in soil cleaning processes

Uniform Convexity of Köthe-Bochner function spaces

Of concern are the Köthe-Bochner function spaces E(X) where X is a real Banach space. Thus, of concern is the uniform convexity on the Köthe-Bochner function space E(X). We show that E(X) is uniformly convex if and only if both spaces E and X are uniformly convex. It is the uniform convexity that is the focal point

Best Simultaneous Approximation in Orlicz Spaces

Let X be a Banach space and let LΦ(I,X) denote the space of Orlicz X-valued integrable functions on the unit interval I equipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, where G is a closed subspace of X, and f1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation in LΦ(I,X) are presented

Some coincidence point results for generalized ( ψ , φ ) -weakly contractions in ordered b-metric spaces

© 2015, Roshan et al.; licensee Springer. In this paper we present some coincidence point results for four mappings satisfying generalized (ψ,φ)-weakly contractive condition in the framework of ordered b-metric spaces. Our results extend, generalize, unify, enrich, and complement recently results of Nashine and Samet (Nonlinear Anal. 74:2201-2209, 2011) and Shatanawi and Samet (Comput. Math. Appl. 62:3204-3214, 2011). As an application of our results, periodic points of weakly contractive mappings are obtained. Also, an example is given to support our results