TY - JOUR
ID - 5841
TI - Near fixed point, near fixed interval circle and their equivalence classes in a $b-$interval metric space
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Joshi, Meena
AU - Tomar, Anita
AD - S. G. R. R. (P. G.) College Dehradun, India
AD - Sri Dev Suman Uttarakhand Vishwavidyalay, Pt. L. M. S. Campus Rishikesh- 249201, Uttarakhand, India
Y1 - 2022
PY - 2022
VL - 13
IS - 1
SP - 1999
EP - 2014
KW - continuity
KW - b−convergence
KW - Completeness
KW - fixed interval circle
KW - null set
KW - T0−topology
DO - 10.22075/ijnaa.2021.21721.2291
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_5841.html
L1 - https://ijnaa.semnan.ac.ir/article_5841_d8a270afaaa21e66ea29c1d0efcfcfbc.pdf
ER -