Fixed Point Formulation Using Exponential Logarithmic Transformations and Its Applications

Abstract

The axioms for a metric $D$ were transformed into axioms of the function $\exp D$, and a new generalized metric called multiplicative metric was introduced in 2008 based on these transformed axioms. A review of a method of converting metric fixed point results through logarithmic transformation to multiplicative metric fixed point results and converting multiplicative metric fixed point results through exponential transformation to metric fixed point results has been presented. Applications of this procedure have also been discussed.

Keywords

• Complete metric space
• Compact metric space
• Hausdorff metric

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