In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

Abstract In this paper I argue that it’s impossible for there to be a single universal theory of meaning language. First, will consider some minimal expressiveness requirements language must meet able express semantic claims. Then in order have unified meaning, these satisfied by which the itself applies to. That is, we would need can its own meaning. It has been well-known since Tarski theorie...

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.