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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 n -periodic mappings in Banach spaces

Jarosław Górnicki, Krzysztof Pupka (2005)

Commentationes Mathematicae Universitatis Carolinae

Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. 29 (1971), 294) and others, which have recently been presented in Chapter 11 of Handbook of Metric Fixed Point Theory (2001).

Fixed point theorems for nonexpansive mappings in modular spaces

Poom Kumam (2004)

Archivum Mathematicum

In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if ρ is a convex, ρ -complete modular space satisfying the Fatou property and ρ r -uniformly convex for all r > 0 , C a convex, ρ -closed, ρ -bounded subset of X ρ , T : C → C a ρ -nonexpansive mapping, then T has a fixed point.

Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Shih-sen Chang, Yu-Qing Chen, Yeol Je Cho, Byung-Soo Lee (1998)

Commentationes Mathematicae Universitatis Carolinae

Let P be a cone in a Hilbert space H , A : P → 2 P be an accretive mapping (equivalently, - A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type - A + T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in L 2 ( Ω ) .

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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