Interpolative \(\alpha_{\mathfrak{p}}\)-contractions in \(C^*\)-algebra valued partial \(b\)-metric spaces: fixed point theorems and applications
Abstract
This study introduces interpolative contraction mappings in \(C^*\)-algebra valued partial \(b\)-metric spaces (\(C^*\)-avp\(b\)ms) through \(\alpha\)-admissible functions. We prove multiple coupled fixed point theorems for these contractions, supported by concrete examples. The theoretical developments find direct application in solving coupled Fredholm integral equations and analyzing homotopy continuation problems, demonstrating their utility in nonlinear analysis.
Copyright © 2026 Appana Bhargavi Siva Prabha, Rajamahanthi Venkata Ganapathi Ravikumar, Bagathi Srinuvasa Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. B. S. Prabha, R. V. G. Ravikumar, B. S. Rao, Interpolative \(\alpha_{\mathfrak{p}}\)-contractions in \(C^*\)-algebra valued partial \(b\)-metric spaces: fixed point theorems and applications, Adv. Fixed Point Theory 16 (2026), 28. https://doi.org/10.28919/afpt/10063
BibTeX
@article{Prabha2026,
author = {Prabha, Appana Bhargavi Siva and Ravikumar, Rajamahanthi Venkata Ganapathi and Rao, Bagathi Srinuvasa},
title = {Interpolative \(\alpha_{\mathfrak{p}}\)-contractions in \(C^*\)-algebra valued partial \(b\)-metric spaces: fixed point theorems and applications},
journal = {Adv. Fixed Point Theory},
volume = {16},
year = {2026},
pages = {28},
doi = {10.28919/afpt/10063}
}