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New fixed point results for \(E\) -metric spaces. (English) Zbl 1516.54038

Summary: A new convergence criteria using the concept of semi-interior points has been defined in \(E\)-metric spaces with non-solid and non-normal set of positive elements \(E^+\) of a real normed space \(E\), also known as a positive cone. Many examples are provided to insure the existence of semi-interior points of \(E^+\) with empty interior. New generalizations of Banach, Kannan and Chatterjea fixed point theorems are proved.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E35 Metric spaces, metrizability
54E40 Special maps on metric spaces
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