Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications
Abstract This paper is committed to introducing some Bihari type inequalities for scalar functions of one independent variable under an initial condition associated with an arbitrary time scale T $\mathbb{T}$. The integrals involve the maximum of an unknown function over a past time interval. We not...
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doaj-d5359f32b5074e8bbc2d4cf0a436ed472020-11-25T03:37:42ZengSpringerOpenBoundary Value Problems1687-27702019-09-012019111710.1186/s13661-019-1259-0Solvability for a class of integral inequalities with maxima on the theory of time scales and their applicationsZareen A. Khan0Department of Mathematics, Princess Nourah bint Abdul Rahman UniversityAbstract This paper is committed to introducing some Bihari type inequalities for scalar functions of one independent variable under an initial condition associated with an arbitrary time scale T $\mathbb{T}$. The integrals involve the maximum of an unknown function over a past time interval. We not only solve some new estimated bounds of a specific class of retarded and nonlinear dynamic inequalities but also derive and unify continuous inequalities along with the corresponding discrete analogs of some known results with ‘maxima’ on time scales. We illustrate some applications of the considered inequalities to represent the advantages of our work. The main results will be proved by utilizing some examination procedures and the basic technique of Keller’s chain rule on time scales.http://link.springer.com/article/10.1186/s13661-019-1259-0Bihari’s inequalityMaximaTime scalesKeller’s chain ruleDynamic equationsDifferential equations with ‘maxima’ |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zareen A. Khan |
spellingShingle |
Zareen A. Khan Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications Boundary Value Problems Bihari’s inequality Maxima Time scales Keller’s chain rule Dynamic equations Differential equations with ‘maxima’ |
author_facet |
Zareen A. Khan |
author_sort |
Zareen A. Khan |
title |
Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications |
title_short |
Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications |
title_full |
Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications |
title_fullStr |
Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications |
title_full_unstemmed |
Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications |
title_sort |
solvability for a class of integral inequalities with maxima on the theory of time scales and their applications |
publisher |
SpringerOpen |
series |
Boundary Value Problems |
issn |
1687-2770 |
publishDate |
2019-09-01 |
description |
Abstract This paper is committed to introducing some Bihari type inequalities for scalar functions of one independent variable under an initial condition associated with an arbitrary time scale T $\mathbb{T}$. The integrals involve the maximum of an unknown function over a past time interval. We not only solve some new estimated bounds of a specific class of retarded and nonlinear dynamic inequalities but also derive and unify continuous inequalities along with the corresponding discrete analogs of some known results with ‘maxima’ on time scales. We illustrate some applications of the considered inequalities to represent the advantages of our work. The main results will be proved by utilizing some examination procedures and the basic technique of Keller’s chain rule on time scales. |
topic |
Bihari’s inequality Maxima Time scales Keller’s chain rule Dynamic equations Differential equations with ‘maxima’ |
url |
http://link.springer.com/article/10.1186/s13661-019-1259-0 |
work_keys_str_mv |
AT zareenakhan solvabilityforaclassofintegralinequalitieswithmaximaonthetheoryoftimescalesandtheirapplications |
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