Abstract
In this paper, multi-valued version of , , , and conditions in Ptolemy metric space are presented. Then the existence of a fixed point for these mappings in a Ptolemy metric space are proved. Finally, some examples are presented. MSC:47H10.
Highlights
1 Introduction The definition of a Ptolemy metric space is introduced by Schoenberg [, ]
Let T be a mapping on a closed subset K of a metric space X which satisfying the SKC, KSC, SCC or CSC condition, d(x, Ty) ≤ d(Tx, x) + d(x, y) holds for x, y ∈ K
Hosseini Ghoncheh and Razani [ ] proved some fixed point theorems for the SCC, SKC, KSC, and CSC conditions in a single-valued version in Ptolemy metric space
Summary
The definition of a Ptolemy metric space is introduced by Schoenberg [ , ]. Let T be a mapping on a subset K of a metric space X, T is said to satisfy C condition if d(x, Tx) ≤ d(x, y) implies d(Tx, Ty) ≤ d(x, y), for all x, y ∈ K .
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