<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly minihedral cone, and scalar weighted cone assuming the cone to be strongly minihedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.</p></abstract>

The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly minihedral cone, and scalar weighted cone assuming the cone to be strongly minihedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.

Results in Strongly Minihedral Cone and Scalar Weighted Cone Metric Spaces and Applications

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly minihedral cone, and...

Results in Strongly Minihedral Cone and Scalar Weighted Cone Metric Spaces and Applications

Published Online: Aug 30, 2021

Page range: 302 - 318

Received: Jun 04, 2020

Accepted: Feb 03, 2021

DOI: https://doi.org/10.2478/amsil-2021-0009

Keywords
Cone metric space, strongly minihedral, normal cone, nonunique fixed point

© 2021 Anita Tomar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Results in Strongly Minihedral Cone and Scalar Weighted Cone Metric Spaces and Applications

Published Online: Aug 30, 2021

Page range: 302 - 318

Received: Jun 04, 2020

Accepted: Feb 03, 2021

DOI: https://doi.org/10.2478/amsil-2021-0009

KeywordsCone metric space, strongly minihedral, normal cone, nonunique fixed point

© 2021 Anita Tomar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Cone metric space, strongly minihedral, normal cone, nonunique fixed point