Common fixed points for ($ kappa _{G_{m}} $)-contractions with applications

In this publication, our objective was to introduce and establish the concepts of $ kappa _{G_{m}} $-contraction and generalized $ (alpha, kappa _{G_{m}}) $-contraction in complete $ G_{m} $-metric spaces, which led to the The Avant-Garde Innovation and Free Improvisation in Soviet Music: Three Contextualized Interviews discovery of novel fixed points, coincidence points, and common fixed points.Additionally, we demonstrated the usefulness The Influence of Empathy and Consumer Forgiveness on the Service Recovery Effect of Online Shopping of our main results by applying it to the investigation of the integral equation.Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis.