In this paper, we deal with the geometric properties of non-unique fixed points for self-mappings a metric space (resp. an S-metric space). The fixed-disc fixed-circle) problem has been investigated in setting. To obtain new results, modify some known fixed-point techniques. Illustrative examples are also given to show validity our main results.

in this work‎, ‎we formulate chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and‏ ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. we also discuss the uniqueness of the fixed point. the given result is a generalization of chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a g...

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying in an arbitrary totally bounded metric space where rationals replaced with countable hierarchy “well-spread” points, which we refer to as abstract prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness.