Generalized Geraghty type mappings on partial metric spaces and fixed point results

Abstract

In the present paper, we introduce generalized Geraghty (Proc Am Math Soc 40:604-608, 1973) mappings on partial metric spaces and give a fixed point theorem which generalizes some recent results appearing in the literature. Mathematics Subject Classification 54H25 · 47H10

Common fixed point theorem of weakly compatible maps in partial metric space

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In this paper, we prove a common fixed point theorem using weakly compatible maps in partial metric space, which generalizes the result of Altun and Sadarangani [12].

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“…Theorem 1.7. [12] Let (X, ρ) be a complete partial metric space and let T : X → X be a self-map. Suppose that there exists β ∈ S such that ρ(Tx, Ty) ≤ β(M(x, y)) max{ρ(x, y), ρ(x, Tx), ρ(y, Ty)} holds for all x, y ∈ X, where…”

Geraghty Type Generalized F-Contractions and Related Applications in Partial b-Metric Spaces

“…Remark 35. Taking ( , ) = ( , ) = 1 and ( ) = in Theorem 28 is akin to Theorem 2.1 of Altun and Sadarangani [17] for -contraction.…”