Uniqueness of Solution for Second Order Nonlinear <i>q</I>-difference Equations With Multi-Point and Integral Boundary Conditions

Abstract

The existence and uniqueness of the solution for the boundary value problem associated with nonlinear second-order q-difference equation is discussed by Banach contraction mapping theorem on b-metric spaces. The problem is converted to an integral equation and investigated via a fixed point problem for an integral operator. Existence and uniqueness conditions for a fixed point of the integral operator are obtained. Moreover, an example is introduced to support the main results.