FIXED POINT THEOREM FOR MAPPING CONVEX CONTRACTING PERIMETER OF TRIANGLE AND APPLICATIONS - Muhammad Khalid; Muhammad Ubaid Ullah; Muhammad Amir Abbas; Sayed Irtaza Hassnain (Policy Research Journal, 2025)
The main aim of this study is to analyze the generalized mapping contraction perimeter of a triangle in metric spaces. We also described a new approach to constructing proofs of some fixed-point theorems in metric spaces, and new tool for proving these theorems. The findings of this thesis consist of two major categories as listed below. In the first section we defined a new mapping known as convex contraction perimeter of a triangle and with its help established few fixed-point theorems in metric spaces. Thus, based on our results, we offered certain fixed - point results in metric spaces and the spaces which are equipped by binary relations. Moreover, we obtained several fixed points conclusions for these contraction mappings with the completion of metric spaces. In the second part of this paper, we used our results to show that a given system of integral equations has a common solution. We also integrated our findings to offer fix-point theorems employing specified mapping. Therefore, our findings add value to the already existing conclusions on the topics of interest within the literature. Finally, we proved the existence of fixed- point results in metric spaces associated with binary relations and have established our main results accompanied by examples.