Some fixed point and best proximity point results on fractals

This thesis is split into five chapters. The first chapter covers the inspiration for the thesis as well as certain background material on fixed point theory, best proximity point theory, and other relevant subjects. In chapter two, we go over the main concepts and notations, along with certain theorems and applications of the fixed point, best proximity point, and Banach contraction principle. We give substantial results on utilising fractals to investigate fixed point theory in chapter three. In chapter four, we offer an intriguing fractal approach based on the best proximity point. Additionally, we present new definitions and notations depending on IFS and PIFS in chapters 3 and 4. Furthermore, we provide several examples to support all of the ideas and notations. Finally,in chapter five, we summarise our significant findings and make proposals for further study.