Best Proximity Points of Contraction Type Operators in Metric and Metric-like Spaces

Abstract

The origin of approximation theory is dated to the middle of twentieth century [49] and rests in the consideration of researchers to setup existence of approximate solutions for the operator equations of the type m = Om. It is significant that the best proximity point theory took off based on work of Eldred and Veeramani [47]. The best proximity points are generally employed to discover approximate solution of the operator equation Om = m, which is optimal, when some contraction O fails to have fixed point. The motivation behind the dissertation is to explore best proximity points of various proximal contraction operators in metric and metric-like spaces. We prove best proximity point theorems for some new generalized multivalued proximal con tractions. We study nonself Presic-type operator and the presence of optimal ap proximate solution for them. Also we give several examples to explain our results. We get some fascinating fixed point outcomes for Presic operator as consequence of our results. We demonstrate best proximity point results in few generalizations of metric space for example; modular metric space and gauge space, for operators satisfying new type of contraction inequality. We introduce fuzzy multiplicative met ric space and prove best proximity points for Feng-Liu type multivalued proximal contraction