New Common Fixed Point Results in Ultrametric Spaces Utilizing Various Contractions and Their Applications to Integral Equations

This study explores fixed points and common fixed points for self‐mappings on ultrametric spaces, regardless of the assumption of spherical completeness. By presenting generalized contractive conditions based on the p ‐adic contraction, we extend classical fixed point results and illustrate their practical use through meticulously crafted examples. We also found some common fixed point solutions to several integral equations, which show how useful our theoretical insights are in real life. The findings advance the evolution of fixed point theory in non‐Archimedean contexts and provide novel insights that augment and expand established theorems in ultrametric analysis.