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Near fixed point, near fixed interval circle and their equivalence classes in a $b-$interval metric space | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 166، دوره 13، شماره 1، خرداد 2022، صفحه 1999-2014 اصل مقاله (459.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21721.2291 | ||
| نویسندگان | ||
| Meena Joshi1؛ Anita Tomar* 2 | ||
| 1S. G. R. R. (P. G.) College Dehradun, India | ||
| 2Sri Dev Suman Uttarakhand Vishwavidyalay, Pt. L. M. S. Campus Rishikesh- 249201, Uttarakhand, India | ||
| تاریخ دریافت: 13 آبان 1399، تاریخ پذیرش: 09 آذر 1400 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Continuity؛ b−convergence؛ completeness؛ fixed interval circle؛ null set؛ T0−topology | ||
| مراجع | ||
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