Ciric type multi-valued $\alpha _{\ast }$-$\eta _{\ast }$-$\theta $-‎contractions on b-metric spaces with applications

Document Type : Research Paper


1 Department of Mathematics, Taiz University, Taiz, Yemen

2 University of Dammam, Department of Mathematics. College of Education of Jubail, P.O: 12020, Industrial Jubail 31961. Saudi Arabia

3 ‎Department of Mathematics‎, ‎International Islamic‎ ‎University‎, ‎H-10‎, ‎Islamabad‎ - ‎44000‎, ‎Pakistan

4 Department of Mathematics, Faculty of Natural Sciences, Centre for Mathematical Research, Khawaja Fareed University of Engineering and Information Technology Rahim Yar Khan, Pakistan

5 Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia


‎In this paper‎, ‎we give sufficient conditions for the existence of solutions‎ of a system of Volterra-type integral inclusion equations using new sort of‎ multi-valued contractions‎, ‎named as generalized multi-valued $\alpha _{\ast‎} ‎$-$\eta _{\ast }$-$\theta $-contractions defined on $\alpha $-complete‎ ‎b-metric spaces‎. ‎We give its relevance to fixed point results‎. ‎We set up an‎ ‎example to elucidate our main results‎.