existence and uniqueness of the solutions of some classes of integral equations c*-algebra-valued b-metric spaces

Introduction/purpose: the aim of the paper is to establish some coupled fixed point results in c*-algebra-valued b-metric spaces. moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. methods: the method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. results: new results were obtained on coupled fixed points in c*-algebra-valued b-metric space. conclusion: the obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations.