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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Oscillation Criteria for Second Order Delay Difference Equations via Canonical Transformations and Some New Monotonic Properties
Author(s):
R. Deepalakhmi, S. Saravanan, J. R. Graef, and E. Thandapani
Department of Interdisciplinary Studies
Tamil Nadu Dr. Ambedkar Law University
Chennai-600113,
India.
profdeepalakshmi@gmail.com
Madras School of Economics,
Chennai-600025,
India.
profsaran11@gmail.com
Department of Mathematics,
University of Tennessee at Chattanooga,
Chattanooga,TN 37403,
USA.
john-graef@utc.edu
Ramanujan Institute for Advanced Study in
Mathematics,
University of Madras,
Chennai - 600 005,
India.
ethandapani@yahoo.co.in
Abstract:
This paper is concerned with second-order linear noncanonical delay difference equations of the form
Δ(μ(t)Δ y(t))+ p(t)y(φ(t))=0.
The authors prove new oscillation criteria by first transforming the equation into canonical form and then obtaining some new monotonic properties of the positive solutions of the transformed equation. By using a comparison with first-order delay difference equations and a generalization of a technique developed by Koplatadze, they obtain their main results. Examples illustrating the improvement over known results in the literature are presented.
Paper's Title:
Orthogonality and ε-Orthogonality in Banach Spaces
Author(s):
H. Mazaheri and S. M. Vaezpour
Faculty of Mathematics, Yazd University, Yazd, Iran
Abstract:
A concept of orthogonality on normed linear space was introduced by Brickhoff,
also the concept of ε-orthogonality was introduced by Vaezpour. In this note, we will consider the relation between these concepts and the dual of
X. Also some results on best coapproximation will be obtained.
Paper's Title:
R-Order Analysis of e-Open Continuous Mapping in Cubic Picture Fuzzy Topological Spaces Author(s):
G. Saravanakumar and K.
Suganthi Department of Mathematics, Department of Mathematics, Abstract:
This paper investigates the structure and properties of {e-continuous mappings}
within the framework of Cubic Picture Fuzzy Topological Spaces (CPFTSs)
under R-order. Building on the foundational role of e-open sets in generalized topological structures, we introduce several classes of continuity-namely
e-continuous, δP-continuous,
δS-continuous a-continuous,
β-continuous, and e*-continuous maps -- and study their interrelationships through logical implications and set-theoretic operations. We establish necessary and sufficient conditions for each type of continuity, along with non-reversible inclusion results supported by counterexamples. Furthermore, we present preservation results involving closure and interior operations under
e-continuous maps and identify conditions under which e-continuity
implies classical R-order continuity. The findings contribute to the refinement of topological structures in fuzzy environments and offer a foundational basis for functional modeling under uncertainty, with applications in decision theory, AI systems, and fuzzy information modeling. Search and serve lasted 0 second(s).
vaezpour@yazduni.ac.ir
hmazaheri@yazduni.ac.ir
1: Paper Source
PDF document
Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology
(Deemed to be University),
Avadi, Chennai-600062,
India.
E-mail: saravananguru2612@gmail.com
Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology
(Deemed to be University),
Avadi, Chennai-600062,
India.
E-mail:
suganthiselvam0980@gmail.com
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