Some New Fixed-point Theorems for Almost Generalized (α, β, γ, ψ₁, ϕ₁*, η, ϑ)-Contractive Mappings in Partial Metric Spaces
Chandni Byapari
*
Dr. C V Raman University, Kargi Road, Kota, Bilaspur, Chhattisgarh, India.
Hiral Raja
Dr. C V Raman University, Kargi Road, Kota, Bilaspur, Chhattisgarh, India.
*Author to whom correspondence should be addressed.
Abstract
In this study, we develop an enhanced fixed-point theorem for self-mappings defined on complete partial metric spaces under an almost generalized (α,β,γ,ψ1*,ϕ1*,η,ϑ) contractive framework. The theorem broadens the scope of existing results by Saluja (2024) through the adoption of a more versatile admissibility structure and the inclusion of additional altering-distance functions, thereby reducing restrictions commonly imposed in earlier formulations. Moreover, the uniqueness assumptions are relaxed, allowing the theorem to cover a wider class of contractive-type mappings. To demonstrate the applicability of the proposed result, we present two corollaries along with a comprehensive numerical example supported by convergence analysis. Together, these components show that the theorem consolidates and strengthens several established fixed-point results reported in the recent literature.
Keywords: Fixed point, α-β-γ admissibility, altering distance functions, partial metric space, generalized contraction, dual perturbation