Filomat· 2015Q2
A new approach to the study of fixed point theory for simulation functions
- 306citations
- Q2SCImago
- 2015year
Short summary
A new class of 'Z-contractions' is introduced, unifying various contraction types and generalizing the Banach contraction principle.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduced simulation functions and Z-contractions for mappings in metric spaces.
- Z-contractions generalize the Banach contraction principle.
- Unifies several known types of contractions.
- Proved related fixed point theorems.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let (X,d) be a metric space and T: X → X be a mapping. In this work, we introduce the mapping ζ:[0,1)x[0,1) → R, called the simulation function and the notion of Z-contraction with respect to Z which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx,Ty) and d(x,y). The related fixed point theorems are also proved.
The authors' abstract, as published at the source. Filomat, 2015 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics