%0 Journal Article
%T Near fixed point, near fixed interval circle and their equivalence classes in a $b-$interval metric space
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Joshi, Meena
%A Tomar, Anita
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 1999-2014
%! Near fixed point, near fixed interval circle and their equivalence classes in a $b-$interval metric space
%K continuity
%K b−convergence
%K Completeness
%K fixed interval circle
%K null set
%K T0−topology
%R 10.22075/ijnaa.2021.21721.2291
%X 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.
%U https://ijnaa.semnan.ac.ir/article_5841_d8a270afaaa21e66ea29c1d0efcfcfbc.pdf