@article {
author = {Joshi, Meena and Tomar, Anita},
title = {Near fixed point, near fixed interval circle and their equivalence classes in a $b-$interval metric space},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {13},
number = {1},
pages = {1999-2014},
year = {2022},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2021.21721.2291},
abstract = {We introduce a novel distance structure called a b−interval metric space to generalize and extend metric interval space. Also, we demonstrate that the collection of open balls, which forms a basis of a b−interval metric space, generates a T0−topology on it. Further, we define topological notions like an open ball, closed ball, b−convergence, b−Cauchy sequence and completeness of the space on a b−interval metric space to create an environment for the survival of a near fixed point and a unique equivalence class of near fixed point. Towards the end, we introduce notions of interval circle, fixed interval circle, its equivalence class and established the existence of a near fixed interval circle and its equivalence interval C−class of near fixed interval circle to study the geometric properties of non-unique equivalence C−classes of nearly fixed interval circles.},
keywords = {continuity,b−convergence,Completeness,fixed interval circle,null set,T0−topology},
url = {https://ijnaa.semnan.ac.ir/article_5841.html},
eprint = {https://ijnaa.semnan.ac.ir/article_5841_d8a270afaaa21e66ea29c1d0efcfcfbc.pdf}
}