The equivalent Cauchy sequences in partial metric spaces.

Hoxha, Elida

doi:10.24297/jam.v12i4.355

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A Necessary and Sufficient Condition For Equivalent1

Introduction1

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2021

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“…Besides, Pasicki [20] and Hoxha and Duraj [21] have given necessary and sufficient conditions in order for a sequence x n n∈N to be Cauchy in dislocated spaces and quasi-dislocated spaces.…”

Section: A Necessary and Sufficient Condition For Equivalentmentioning

confidence: 99%

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Equivalent Cauchy Sequences in $(q_{1})$

Sila

Duraj

Hoxha

2021

Journal of Mathematics

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This paper introduces the concept of q 1 , q 2 -quasi metric-like space X , p and delves into some topological properties of it. A necessary and sufficient condition related to equivalent Cauchy sequences and Cauchy sequences in X , p have been proved. Furthermore, the results of the fixed point are shown in the setting of q 1 , q 2 -quasi metric-like space as applications of conditions of equivalent Cauchy sequences. Besides, some instances are inclined to epitomize the examined consequences.

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Section: A Necessary and Sufficient Condition For Equivalentmentioning

confidence: 99%

“…In 1983, Leader [19] obtained a necessary and sufficient condition as a characterization of equivalent Cauchy sequences in the metric space. Nevertheless, the generalizations of the consequences are found in spaces, [20,21], obtaining fixed-point results for the contractive function of Mein-Keeler type.…”

Section: Introductionmentioning

confidence: 99%