TY  - JOUR
T1  - A Robust Approach About Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces
AU  - Candan, Murat
PY  - 2024
DA  - January
DO  - 10.54974/fcmathsci.1303769
JF  - Fundamentals of Contemporary Mathematical Sciences
JO  - FCMS
PB  - Mustafa UÇKUN
WT  - DergiPark
SN  - 2717-6185
SP  - 48
EP  - 59
VL  - 5
IS  - 1
LA  - en
AB  - In this new study, whichdeals with the different properties of $\ell_{p}(\widehat{F}(r,s))$ $(1\leqp
KW  - Sequence spaces
KW  - Fibonacci numbers
KW  - Compact operators
KW  - Hausdorff measure of noncompactness
CR  - [1] Başar F., Summability Theory and Its Applications, 2nd Ed., CRC Press, Taylor and Francis Group,
2022.
CR  - [2] Başar F., Dutta H., Summable Spaces and Their Duals, Matrix Transformations and Geometric
Properties, CRC Press, Taylor and Francis Group, Monographs and Research Notes in Mathematics,
2020.
CR  - [3] Mursaleen M., Başar F., Sequence Spaces: Topics in Modern Summability Theory, CRC Press, Taylor
and Francis Group, Series: Mathematics and Its Applications, 2020.
CR  - [4] Mursaleen M., Applied Summability Methods, Springer Briefs, 2014.
CR  - [5] De Malafosse B., Malkowsky E., Rakocevic V., Operators Between Sequence Spaces and Applications,
Springer, 2022.
CR  - [6] Başar F., Altay B., On the space of sequences of p−bounded variation and related matrix mappings,
Ukrains; Matematychnyi Zhurnal, 55(1), 136-147, 2003.
CR  - [7] Altay B., Başar F., Mursaleen M., On the Euler sequence spaces which include the spaces ℓp and ℓ∞,
Information Sciences, 176(10), 1450-1462, 2006.
CR  - [8] Altay B., Başar F., Certain topological properties and duals of the matrix domain of a triangle matrix
in a sequence space, Journal of Mathematical Analysis and Applications, 336(1), 632-645, 2007.
CR  - [9] Başar F., Malkowsky E., Altay B., Matrix trasformations on the matrix domains of triangles in
the spaces of strongly C1−summable and bounded sequences, Publicationes Mathematicae Debrecen,
73(1-2), 193-213, 2008.
CR  - [10] Başarır M., Başar F., Kara E.E., On the spaces of Fibonacci difference absolutely p−summable, null
and convergent sequences, Sarajevo Journals of Mathematics, 12(25), 167-182, 2016.
CR  - [11] Banaś J., Mursaleen M., Sequence Spaces and Measures of Noncompactness with Applications to
Differential and Integral Equations, Springer, 2014.
CR  - [12] Wilansky A., Summability Through Functional Analysis, North-Holland Mathematics Studies 85,
Elsevier Science Publishers, 1984.
CR  - [13] Goldenštein L.S., Gohberg I.T., Markus A.S., Investigations of some properties of bounded linear
operators in connection with their q -norms, Učen Zap Kishinevsk Universty, 29, 29-36, 1957.
CR  - [14] Goldenštein L.S., Markus A.S., On a measure of noncompactness of bounded sets and linear operators,
Studies in Algebra and Mathematical Analysis, 45-54, 1965.
CR  - [15] Kuratowski K., Sur les espaces complets, Fundamenta Mathematicae, 15, 301-309, 1930.
CR  - [16] Darbo G., Punti uniti in transformazioni a condominio non compatto, Rendiconti del Seminario
Matematico della Università di Padova, 24, 84-92, 1955.
CR  - [17] Akhmerov R.R., Kamenskij M.I., Potapov A.S., Rodkina A.E., Sadovskii B.N., Measures of Noncompactness
and Condensing Operators, Operator Theory Advances and Applications, 1992.
CR  - [18] Ayerbe Toledano J.M., Domínguez Benavides T., López Azedo G., Measures of Noncompactness in
Metric Fixed Point Theory, Operator Theory Advances and Applications, 1997.
CR  - [19] Banaś J., Goebel K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and
Applied Mathematics, 60, Marcel Dekker, 1980.
CR  - [20] Malkowsky E., Rakočević V., An introduction into the theory of sequence spaces and measures of
noncompactness, Zbornik Radova, Matematički Institut SANU, 9(17), 143-234, 2000.
CR  - [21] Alotaibi A., Malkowsky E., Mursaleen M., Measure of noncompactness for compact matrix operators
on some BK spaces, Filomat, 28, 1081-1086, 2014.
CR  - [22] Başarır M., Kara E.E., On compact operators on the Riesz B(m) -difference sequence spaces, Iranian
Journal of Science and Technology, 35(A4), 279–285, 2011.
CR  - [23] Başarır M., Kara E.E., On some difference sequence spaces of weighted means and compact operators,
Annals of Functional Analysis, 2, 114-129, 2011.
CR  - [24] Başarır M., Kara E.E., On the B-difference sequence space derived by generalized weighted mean and
compact operators, Journal of Mathematical Analysis and Applications, 391, 67-81, 2012.
CR  - [25] Kara E.E., Başarır M., On compact operators and some Euler B(m)-difference sequence spaces,
Journal of Mathematical Analysis and Applications, 379, 499-511, 2011.
CR  - [26] De Malafosse B., Malkowsky E., Rakočević V., Measure of noncompactness of operators and matrices
on the spaces c and c0 , International Journal of Mathematics and Mathematical Sciences, 2006, 1-5,
2006.
CR  - [27] De Malafosse B., Rakočević V., Applications of measure of noncompactness in operators on the spaces
sα, Journal of Mathematical Analysis and Applications, 323, 131-145, 2006.
CR  - [28] Mursaleen M., Karakaya V., Polat H., Simsek N., Measure of noncompactness of matrix operators on
some difference sequence spaces of weighted means, Computers and Mathematics with Applications,
62, 814-820, 2011.
CR  - [29] Mursaleen M., Mohiuddine S.A., Applications of measures of noncompactness to the infinite system
of differential equations in ℓp spaces, Nonlinear Analysis: Theory, Methods and Applications, 75,
2111-2115, 2012.
CR  - [30] Mursaleen M., Noman A.K., Compactness by the Hausdorff measure of noncompactness, Nonlinear
Analysis: Theory, Methods and Applications, 73, 2541-2557, 2010.
CR  - [31] Mursaleen M., Noman A.K., Compactness of matrix operators on some new difference sequence spaces,
Linear Algebra and Its Applications, 436, 41-52, 2012.
CR  - [32] Koshy T., Fibonacci and Lucas Numbers with Applications, Wiley, 2001.
CR  - [33] Kara E.E., Some topological and geometrical properties of new Banach sequence spaces, Journal of
Inequalities and Applications, 38, 15 pages, 2013.
CR  - [34] Candan M., Kara E.E., A study on topological and geometrical characteristics of new Banach sequence
spaces, Gulf Journal of Mathematics 3(4), 67-84, 2015.
CR  - [35] Alotaibi A., Mursaleen M., Alamri B.A.S., Mohiuddine S.A., Compact operators on some Fibonacci
difference sequence spaces, Journal of Inequalities and Applications, 203, 8 pages, 2015.
CR  - [36] Kara E.E., Başarır M., Mursaleen M., Compactness of matrix operators on some sequence spaces
derived by Fibonacci numbers, Kragujevac Journal of Mathematics, 39(2), 217-230, 2015.
CR  - [37] Malkowsky E., Rakočević V., On matrix domains of triangles, Applied Mathematics and Computation,
187, 1146-1163, 2007.
UR  - https://doi.org/10.54974/fcmathsci.1303769
L1  - https://dergipark.org.tr/en/download/article-file/3169669
ER  -