Characterization and Application of Fixed Point Theorems for 3-Self Mappings in Generalized Metric Spaces

In this paper, we investigate new contraction results for 3-self-mappings on generalized metric spaces (GM-spaces) and develop and highlight the importance of several particular common fixed point (CFP) theorems. Our study contributes to the theoretical framework of fixed point theory by highlighting the existence of such points and thoroughly proving their uniqueness. As a practical application of our theoretical findings, we design and analyze a convincing case including 3-self mappings to further support the uniqueness of a CFP for generalized contractions in the given space. We also provide a solid and perceptive application pertaining to nonlinear integral equations to further support the wider applicability of our primary contributions, demonstrating the usefulness of our discoveries in mathematical analysis and beyond. An excellent example is developed for better understanding the results.