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http://dx.doi.org/10.14317/jami.2019.329

EXISTENCE OF THE SOLUTION OF COUNTABLY INFINITE SYSTEM OF DIFFERENTIAL EQUATIONS IN SEQUENCE SPACES mp(𝜙) AND np(𝜙) WITH THE HELP OF MEASURE OF NON-COMPACTNESS  

KHAN, MOHD SHOAIB (Department of Mathematics, South Asian University)
UDDIN, IZHAR (Department of Mathematics, Jamia Millia Islamia)
LOHANI, Q.M. DANISH (Department of Mathematics, South Asian University)
Publication Information
Journal of applied mathematics & informatics / v.37, no.5_6, 2019 , pp. 329-339 More about this Journal
Abstract
The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.
Keywords
Sequence spaces $m^p(\phi)$ and $n^p(\phi)$; Banach space; Countably infinite system of differential equations; Measure of non-compactness;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 E. Malkowsky, Modern functional analysis in theory of sequence spaces and matrix transformations, (2008).
2 E. Malkowsky and V. Rakocevic, An introduction into the theory of sequence spaces and measures of noncompactness, Zbornik radova (2000), no. 17, 143-234.
3 M. Mursaleen, Some geometric properties of a sequence space related to l (p), Bulletin of the Australian Mathematical Society 67 (2003), no. 2, 343-347.   DOI
4 M. Mursaleen and S.A. Mohiuddine, Applications of measures of noncompactness to the infinite system of differential equations in p spaces, Nonlinear Analysis: Theory, Methods & Applications 75 (2012), no. 4, 2111-2115.   DOI
5 Mohammad Mursaleen, Application of measure of noncompactness to infinite system of differential equations, Can. Math. Bull 56 (2013), no. 2, 388-394.   DOI
6 Jozef Banas and Millenia Lecko, Solvability of infinite systems of differential equations in banach sequence spaces, Journal of Computational and Applied Mathematics 137 (2001), no. 2, 363-375.   DOI
7 Jozef Banas and Kishin Sadarangani, Compactness conditions and strong subdifferentiability of a norm in geometry of banach spaces, Nonlinear Analysis: Theory, Methods & Applications 49 (2002), no. 5, 623-629.   DOI
8 Richard Bellman, Augustine O Esogbue, and Ichiro Nabeshima, Mathematical aspects of scheduling and applications: Modern applied mathematics and computer science 4, Elsevier, 2014.
9 V.A. Khan, Some matrix transformations and measures of noncompactness, Rendiconti del Circolo Matematico di Palermo 60 (2011), no. 1-2, 153-160.   DOI
10 V.A. Khan and M. Mursaleen, Applications of measures of noncompactness in matrix transformations, Applied Mathematics Letters 7 (2006), no. 19, 599-606.
11 A Voigt, Line method approximations to the cauchy problem for nonlinear parabolic differential equations, Numerische Mathematik 23 (1974), no. 1, 23-36.   DOI
12 K.P. Persidski, Countable systems of differential equations and stability of their solutions iii: Fundamental theorems on stability of solutions of countable many differential equations, Izv. Akad. Nauk Kazach. SSR 9 (1961), 11-34.
13 K.P. Persidskii, Countable systems of differential equations and stability of their solutions, Izv. Akad. Nauk Kazach. SSR 7 (1959), 52-71.
14 W.L.C. Sargent, Some sequence spaces related to the lp spaces, Journal of the London Mathematical Society 1 (1960), no. 2, 161-171.   DOI
15 B.C. Tripathy, N.L. Braha, and A.J. Dutta, A new class of fuzzy sequences related to the lp space defined by orlicz function, Journal of Intelligent & Fuzzy Systems 26 (2014), no. 3, 1273-1278.   DOI
16 B.C. Tripathy and Mausumi Sen, On a new class of sequences related to the space $l_p$, Tamkang Journal of Mathematics 33 (2002), no. 2, 167-172.   DOI
17 W. Walter, Differential and integral inequalities. translated by lisa rosenblatt and lawrence shampine, Springer-Verlag, 1970.
18 O.A. Zautykov and K.G. Valeev, Infinite systems of differential equations, Izdat. Akad.Nauka Kazach SSR, Alma-Ata (1974).
19 Klaus Deimling and Vangipuram Lakshmikantham, Existence and comparison theorems for differential equations in banach spaces, Nonlinear Analysis: Theory, Methods & Applications 3 (1979), no. 5, 569-575.   DOI
20 Serkan Demiriz, Applications of measures of noncompactness to the infinite system of differential equations in bvp spaces, Electronic Journal of Mathematical Analysis and Applications 5 (2017), no. 1, 313-320.
21 M.S. Khan, Q.M. Danish Lohani, and M. Mursaleen, A novel intuitionistic fuzzy similarity measure based on double sequence by using modulus function with application in pattern recognition, Cogent Mathematics 4 (2017), no. 1, 1385374.   DOI
22 Einar Hille, Pathology of infinite systems of linear first order differential equations with constant coefficients, Annali di Matematica Pura ed Applicata 55 (1961), no. 1, 133-148.   DOI
23 Mouffak Benchohra, Samira Hamani, Juan Jose Nieto, and Boualem Attou Slimani, Existence of solutions to differential inclusions with fractional order and impulses., Electronic Journal of Differential Equations (EJDE)[electronic only] 2010 (2010), Paper-No.
24 Lazhar Bougoffa and Ammar Khanfer, Existence and uniqueness theorems of second-order equations with integral boundary conditions, Bulletin of the korean mathematical society 55 (2018), no. 3, 899-911.   DOI
25 Murat Karakas, Muhammed Cinar, and Mikail Et, Some geometric properties of a new sequence space, J. Comput. Anal. Appl 15 (2013), 23-31.
26 M.S. Khan, B.A.S. Alamri, M Mursaleen, and QM Danish Lohani, Sequence spaces m (${\varphi}$) and n (${\varphi}$) with application in clustering, Journal of ineqalities and applications (2017).