On new fixed point results in $E_{b}$-metric spaces

Jamnian Nantadilok

Abstract


In this paper, we introduce the concepts of an extended cyclic Banach contraction and an extended cyclic orbital $\mathcal{F}$-expanding contraction. Thereby, we prove pertinent fixed point theorems  in an extended $b$-metric space (simply $E_{b}$-metric space). Moreover, we present the characterization of the Hardy and Rogers mapping theorem for (a pair of) non-self maps, which gives a positive answer to the question raised by C. Boateng Ampadu \cite{A} (Fixed Point Theory, 19(2018), No. 2, 449-452DOI: 10.24193/fpt-ro.2018.2.35).

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