scholarly journals Decomposition of abstract linear operators in Banach spaces

2021 ◽  
pp. 2-12
Author(s):  
Kyriaki Tsilika
Keyword(s):  
Banach Spaces ◽  
Direct Method ◽  
Relevant Literature ◽  
Research Result ◽  
Sufficient Conditions ◽  
Initial Boundary ◽  
Decomposition Methods ◽  
Linear Operators ◽  
Main Research ◽  
Symbolic Calculations

In this paper we investigate a class of integro-differential equations οn a Banach space with nonlocal and initial boundary conditions in terms of an abstract operator equation             B1 x=Ax-S0 F(A x)-G0 Φ(Ax)=f ,x∈D(B1)            (1)    where  A, A are linear abstract operators,  S0, G0 are vectors and Φ, F the functional vectors. The operator B1 under study has a decomposition of the form B1=B0 B  with B and B0  being different abstract linear operators of special forms. Methods. Extensions of operators on Banach spaces are used. The Decomposition Method proposed here is essentially different from other Decomposition Methods in the relevant literature. Results. Our main research result is the existence and uniqueness of solution of  and its representation in the closed form. The necessary and sufficient conditions for the correctness of the operator  are intermediate, secondary results. Overall, a direct method analytically solving problem (1) is proposed, in an algorithmic procedure that is reproducible in any program of symbolic calculations. The stages of the solution method are illustrated by three examples. Computer algebra system Mathematica is employed to demonstrate the solution outcomes.

The Hahn-Banach theorem for non-Archimedean-valued fields

1952 ◽  
Vol 48 (1) ◽  
pp. 41-45 ◽  
Author(s):  
A. W. Ingleton
Keyword(s):  
Banach Spaces ◽  
Normed Linear Space ◽  
General Theorem ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Necessary Condition ◽  
Linear Functionals ◽  
Banach Theorem ◽  
Necessary And Sufficient ◽  
Special Case

1. The Hahn-Banach theorem on the extension of linear functionals holds in real and complex Banach spaces, but it is well known that it is not in general true in a normed linear space over a field with a non-Archimedean valuation. Sufficient conditions for its truth in such a space have been given, however, by Monna and by Cohen‡. In the present paper, we show that a necessary condition for the property is that the space be totally non-Archimedean in the sense of Monna, and establish a necessary and sufficient condition on the field for the theorem to hold in every totally non-Archimedean space over the field. This result is obtained as a special case of a more general theorem concerning linear operators, which is analogous to a theorem of Nachbin ((6), Theorem 1) concerning operators in real Banach spaces.

scholarly journals On uniform exponential trisplitting for cocycles of linear operators in Banach spaces

2018 ◽  
Vol 56 (2) ◽  
pp. 81-103
Author(s):  
Larisa Elena Biriş ◽  
Claudia Luminiţa Mihiţ ◽  
Traian Ceauşu ◽  
Ioan-Lucian Popa
Keyword(s):  
Banach Spaces ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Type A ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Skew Product ◽  
Exponential Trichotomy ◽  
Necessary And Sufficient

AbstractThe aim of this paper is to study the concept of uniform exponential trisplitting for skew-product semiflow in Banach spaces. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. We obtain necessary and sufficient conditions for this concept of Datko’s type. a character-isation in terms of Lyapunov functions is provided. The results are obtained from the point of view of the projector families, i.e. invariant and strongly invariant.

scholarly journals Operator Ideal of Cesaro Type Sequence Spaces Involving Lacunary Sequence

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Awad A. Bakery
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Lacunary Sequence ◽  
Operator Ideal ◽  
Linear Operators ◽  
Approximation Numbers ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Type Sequence

The aim of this paper is to give the sufficient conditions on the sequence spaceCesθ,pdefined in Lim (1977) such that the class of all bounded linear operators between any arbitrary Banach spaces withnth approximation numbers of the bounded linear operators inCesθ,pform an operator ideal.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

THE IMPACT OF SERVICE QUALITY ON BRAND LOYALTY OF DTAC SELULER SERVICE USERS

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Debby Arisandi
Keyword(s):  
Service Quality ◽  
Customer Service ◽  
Service Provider ◽  
Brand Loyalty ◽  
Service Industry ◽  
Positive Impact ◽  
Relevant Literature ◽  
Field Research ◽  
Main Research ◽  
The Impact

<p>Purpose- In the GSM seluler telephony sector, the main condition for protecting the subscriber base is to win customer to be loyalty, a key necessity for the maintenance of a brand loyalty in the long term. To achieve this aim, service quality must be measured and identified. This paper’s aim is to measure the effects of service quality towards brand loyalty on DTAC seluler service provider. This study will explore the relationship between service quality and brand loyalty in the seluler service industry.</p><p>Design/methodology/approach- The main research target sample covered 200 seluler phone users in Prince of Songka University, Hatyai campus. Field research was conducted. The questionnaire was formed by a synthesis of existing constructs in relevant literature. Reliability tests, descriptive statistic, and regressions analyses were performed to both confirm scale reliability and answer the research questions. The data were analysed by moderated regression analysis to test the hypotheses.</p><p>Findings- The findings of this study show that an overall service quality directly affects brand loyalty. Network quality, customer service, pricing structure and billing system are the service quality dimensions that have significant positive influence on brand loyalty, which in turn has a significant positive impact on brand loyalty 43,5%. Therefore, it plays a crucial role in winning customer loyalty.</p><p>Originality/value- It is of great importance for seluler operators in a mature market such as that of Thailand, to understand what the drivers of brand loyalty are. The present study produced useful findings, which can be utilized by seluler service provider managers, in their effort to develop and implement successful brand loyalty strategies. With respect to the findings, pricing structure has the most importance than others dimensions of service quality which provides positive outcomes on brand loyalty, not only in the present but also in the future. So, the effect of pricing structure on brand loyalty becomes greater than the effect of others dimenstions of service quality. Therefore, any GSM operator who wishes to preserve its existing subscriber base should concentrate on winning its subscribers’ loyalty, especially for DTAC.</p>Keywords- Seluler Services, Brand Loyalty, Service Quality

Linear Operators in Banach Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Fredholm Maps

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so as to derive important results later in the book.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

scholarly journals Blowing-up solutions of the time-fractional dispersive equations

2021 ◽  
Vol 10 (1) ◽  
pp. 952-971
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Berikbol T. Torebek
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Nonlinear Capacity ◽  
Blowing Up ◽  
De Vries ◽  
Initial Boundary Value

Abstract This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.

scholarly journals Sets of periods for chaotic linear operators

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
J. A. Conejero ◽  
F. Martínez-Giménez ◽  
A. Peris ◽  
F. Rodenas
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Complete Characterization ◽  
Linear Operators

AbstractWe provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

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