Analysis of Fixed Point Iterations on Various Spaces

Abstract

The fixed point theory is a widely used concept for the solution of the real world problems that can be modelled into non-linear differential and integral equations. The iterative processes are the road map that are used for the achievement of the fixed point. A wide range of literature shows that fixed point convergence of iterative schemes has been extensively studied and many researchers have given significant results in this regard. The idea of complex valued metric space was formulated in 2011 and since then the whole fixed point theory has flourished in a new direction with many useful results. There has been a number of variations and extensions of this space with new conditions and parameters being introduced. Further, with the conception of every new kind of space, the previous results have been given new formations under them. The crux of this study lies in the fact that there has been a huge opportunity to establish new results in this area. This has been the motivation to explore this branch for new results. Also, some iteration schemes have been analyzed for the current study. For different spaces, iterations have been used for proving some convergence results and then their rate of convergence have been analyzed. newline