Some Functional Sections in Topological Sequence Spaces

Ahmet Ocak Akdemi̇r, Merve Temizer Ersoy, Hasan Furkan, Maria Alessandra Ragusa

Type: Article

Publication Date: 2022-07-09

Citations: 6

DOI: https://doi.org/10.1155/2022/6449630

Abstract

Summability is a particularly fertile field for functional analysis application. Summability through functional analysis has become one of the most fascinating disciplines since it contains both interesting and challenging issues. In this paper, we aim to introduce four new sectional properties for topological sequence spaces: sectional weakly absolute convergence (WAC), sectional weak boundedness (WB), sectional weakly <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><mi>p</mi></math> -absolute convergence <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><mfenced open="(" close=")"><mrow><msub><mrow><mtext>W</mtext></mrow><mrow><mi>p</mi></mrow></msub><mtext>AC</mtext></mrow></mfenced></math> , and sectional weakly bounded variation (WBV). We have, also, investigate some of their relations and identities.

Locations

Journal of Function Spaces - View - PDF

Similar Works

Action	Title	Year	Authors
+	Sequence Spaces	2022	Martin Buntinas
+	The Rate of Sectional entire sequence spaces	2012	N. Gurumoorthy K. Chandrasekhara Rao
+ PDF Chat	<b>The Rate of Sectional entire sequence spaces</b> - doi: 10.5269/bspm.v30i2.14304	1970	N. Gurumoorthy K. Chandrasekhara Rao
+	SECTIONS OF MEASURABLE FUNCTIONS	2018	P. Jisna Raji Pilakkat
+	On convergence of sections of sequences in Banach spaces	2000	Shem Aywa Jan Fourie
+	On l1-Invariant Sequence Spaces	2001	Karl-Goswin Grosse-Erdmann
+	Remark to the definition of the limit of a function in terms of the sequences	2018	O. O. Kurchenko Olga Syniavska
+	On Toeplitz sections in sequence spaces	1975	Martin Buntinas
+	Analysis in functional spaces	1984	Jean Bourgain A. Pełczyński I. A. Komarchev B. Makarov P. Wojtaszczyk Peter G. Casazza Э. М. Семенов P. Wojtaszczyk Peter W. Jones Э. М. Семенов
+ PDF Chat	Variation norm convergence of function sequences	1974	Randolph Constantine
+	Functional Banach Limits	2021	Gokulananda Das Sudarsan Nanda
+ PDF Chat	A Projective Description of Weighted Inductive Limits	1982	Klaus D. Bierstedt Reinhold Meise W. H. Summers
+ PDF Chat	Relative Uniform Convergence of Sequence of Functions Related to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi>ℓ</a:mi></a:mrow><a:mrow><a:mi>p</a:mi></a:mrow></a:msub></a:math>-Spaces Defined by Orlicz Functions	2024	Diksha Debbarma Mustafa M. Mohammed Binod Chandra Tripathy Awad A. Bakery
+	On the strong convergence in some sequence spaces	2002	A. Waszak
+	Preliminaries	2023	Rafaël Correa Abderrahim Hantoute Marco A. López
+	The linear topology associated with weak convergence of probability measures	2013	Liang Hong
+ PDF Chat	The Linear Topology Associated with Weak Convergence of Probability Measures	2014	Liang Hong
+ PDF Chat	Subsequences of Real Valued Sequences and Convergence	2021	Leila Miller-Van Wieren
+	Results from Functional Analysis and Function Spaces	2006
+	Sectionwise properties and measurability of functions of two variables	1982	Miklós Laczkovich G. Petruska

Works That Cite This (6)

Action	Title	Year	Authors
+ PDF Chat	The multiplicity and asymptotic forms of eigenvalues of vectorial diffusion equations with some certain assumptions	2023	Abdullah Ergün
+	Generalized derivatives and Laplace transform in (<i>k</i>,<i>ψ</i>)‐Hilfer form	2023	Yasemin Başçı Adil Mısır Süleyman Öğrekçi
+	On some new Rhaly sequence spaces and Rhaly Sections in BK-space	2024	A. C. Das Bilâl Altay
+	Stable critical points of even functionals on the Banach space and applications	2023	Xiaofei Cao Guowei Dai Siyu Gao Qingbo Liu
+	Uniqueness and stability analysis to a system of nonlocal partial differential equations related to an epidemic model	2023	Wenbing Wu
+	$ N $-dimensional fractional Hardy operators with rough kernels on central Morrey spaces with variable exponents	2023	Chenchen Niu Hongbin Wang

Works Cited by This (12)

Action	Title	Year	Authors
+ PDF Chat	On unconditional section boundedness in sequence spaces	1977	John J. Sember
+	On l1-Invariant Sequence Spaces	2001	Karl-Goswin Grosse-Erdmann
+	Certain topological properties and duals of the domain of a triangle matrix in a sequence space	2007	Bilâl Altay Feyzı Başar
+ PDF Chat	The Unrestricted Section Properties of Sequences	1979	John J. Sember Marc Raphael
+	Current Topics in Summability Theory and Applications	2016	Hemen Dutta Β. E. Rhoades
+	XI.—On Unconditional Convergence in Topological Vector Spaces	1969	A. P. Robertson
+	Banach Space Theory	2010	Marián Fabian Petr Habala Petr Hájek Vicente Montesinos Václav Zizler
+	An Introductory Course in Summability Theory	2017	Ants Aasma H. N. Dutta P.N. Natarajan
+ PDF Chat	Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability	2021	Merve Temizer Ersoy
+	On Fredholm-Type Integral Equations in Topological Hölder Spaces	2021	Merve Temizer Ersoy Hasan Furkan