Some existence results for a nonlinear q-integral equations via M.N.C and fixed point theorem Petryshyn

The paper focuses on establishing sufficient conditions for the existence of the solutions in some functional q -integral equations, particularly in Banach spaces. In this method, the technique of measures of noncompactness and Petryshyn’s fixed point theorem in Banach space is used. We provide some examples of equations, which confirm that our result is applicable to a wide class of integral equations.