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Research Paper | Mathematics | Volume 15 Issue 6, June 2026 | Pages: 960 - 967 | India
Fixed Point Theorems Under an Expansive Rational Condition in Ab- Metric Spaces
Abstract: We introduce an expansive rational condition for self maps acting on Ab-metric spaces and study its consequence for fixed point existence and uniqueness .While contraction condition are classical in fixed point theory, expansive condition when paired with structural hypotheses such as inevitability or contractive behavior of an inverse or an iterate also yield fixed points in generalized metric setting .We present a main existence and uniqueness theorem that applies when the inverse map satisfies a linear rational contractive :three corollaries treat iterates, commuting maps and a multivalued selection case. Several examples illustrate the hypotheses. The setting generalizes existing results on Ab-metric and related generalized metric spaces.
Keywords: Ab-metric space, expansive rational condition, fixed point, linear rational contraction, generalized metric spaces
How to Cite?: Rajesh Kumar Nagwanshee, Manoj Ughade, M. S. Chauhan, "Fixed Point Theorems Under an Expansive Rational Condition in Ab- Metric Spaces", Volume 15 Issue 6, June 2026, International Journal of Science and Research (IJSR), Pages: 960-967, https://www.ijsr.net/getabstract.php?paperid=SR26609152746, DOI: https://dx.doi.org/10.21275/SR26609152746