A Novel Approach to Some Proximal Contractions with Examples of Its Application

In this article, we will introduce a new generalized proximal θ-contraction for multivalued and single-valued mappings named (f−θκ)CP-proximal contraction and (f−θκ)BP-proximal contraction. Using these newly constructed proximal contractions, we will establish new results for the coincidence best proximity point, best proximity point, and fixed point for multivalued mappings in the context of rectangular metric space. Also, we will reduce these contractions for single-valued mappings, named (θκ)CP-proximal contraction and (θκ)BP-proximal contraction, to establish results for the coincidence proximity point, best proximity point, and fixed point results. We will give some illustrated examples for our newly generated results with graphical representations. In the last section, we will also find the solution to the equation of motion by using our defined results.