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Fixed point theorems for hybrid pair of weak compatible mappings in partial metric spaces

Santosh Kumar, Johnson Allen Kessy (2023)

Mathematica Bohemica

The notions of compatible mappings play a crucial role in metrical fixed point theory. Partial metric spaces are a generalization of the notion of a metric space in the sense that distance of a point from itself is not necessarily zero. In this paper, we prove coincidence and fixed point theorems for a pair of single-valued and multi-valued weak compatible mappings on a complete partial metric space. Our main results generalize, in particular, the results of Kaneko and Sessa (1989), Pathak (1995)...

Fixed point theorems for set-valued Y-contractions

Ioan A. Rus, Adrian Petruşel, Gabriela Petruşel (2007)

Banach Center Publications

The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.

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