FIXED POINT AND COUPLED FIXED POINT THEOREMS FOR A NEW GENERALIZED S -PATA-TYPE CONTRACTION IN S-METRIC SPACE WITH APPLICABILITY TO BOUNDARY VALUE PROBLEM
DOI:
https://doi.org/10.65463/jprm.2026327.Keywords:
Fixed point, fixed point theorems, boundary value problemsAbstract
This study advances the field of fixed point theory within the framework of S metric space. We first refine the notion of a generalized S-Pata-type contraction by introducing supplementary cross terms into the contractive condition. Within this extended setting, we derive new fixed point theorems that both enhance the earlier results. It addition to widen the applicability of our contractive mappings , we formulate and analyze a coupled fixed point theorem for S Pata-type contraction, where condition ensuring existence and uniqueness. Finally, the effectiveness of our approach is demonstrated through applications to ordinary differential equations, in particular a boundary value problem for a second-order equation, thereby underlining the practical relevance of the theoretical developments presented.
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