EXISTENCE OF FIXED-POINT FOR A GENERALIZED CONTRACTION IN S-METRIC SPACES

Abstract

This paper investigates the existence of fixed points for a class of generalized contractions in complete S-metric spaces. We explore several types of contraction conditions and provide an enriched theoretical framework supported by examples. The paper includes novel results extending the Banach contraction principle, altering distance function approaches, and weakly compatible maps to the context of S-metric spaces. Moreover, new classes of contraction mappings such as cyclic contractions, common fixed points for pairs of commuting mappings, and generalized Φ-type contractions are explored and discussed. Our findings offer a unifying structure that links various fixed-point theorems under a broader umbrella, enhancing their applicability to diverse problems in differential equations, optimization, and dynamical systems. The introduction of new contraction conditions helps in the relaxation of hypotheses, making our results applicable in settings where classical conditions fail. We also extend results for bounded S-metric spaces and establish common fixed-point theorems for pairs of weakly compatible maps using altering distance functions and comparison functions. With rich examples and illustrative explanations, the results in this paper contribute significantly to the growing literature on fixed point theory in generalized metric spaces.