Partial Differentiation on Time Scales

Böhner, Martin; Georgiev, Svetlin G.

doi:10.1007/978-3-319-47620-9_6

Cited by 42 publications

(42 citation statements)

References 7 publications

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“…The two-variable time scale calculus and multiple integration have been introduced in [23,24]. In what follows, we provide the two-dimensional versions of Theorems 4 and 5.…”

Section: Resultsmentioning

confidence: 99%

A Parameter-Based Ostrowski–Grüss Type Inequalities with Multiple Points for Derivatives Bounded by Functions on Time Scales

Kermausuor

Nwaeze

2018

Mathematics

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In this paper, we present some Ostrowski–Grüss-type inequalities on time scales for functions whose derivatives are bounded by functions for k points via a parameter. The 2D versions of these inequalities are also presented. Our results generalize some of the results in the literature. As a by-product, we apply our results to the continuous and discrete calculus to obtain some interesting inequalities in this direction.

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“…The two-variable time scale calculus and multiple integration have been introduced in [23,24]. In what follows, we provide the two-dimensional versions of Theorems 4 and 5.…”

Section: Resultsmentioning

confidence: 99%

A Parameter-Based Ostrowski–Grüss Type Inequalities with Multiple Points for Derivatives Bounded by Functions on Time Scales

Kermausuor

Nwaeze

2018

Mathematics

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“…It is expected that the reader must be acquainted with the information and fundamental ideas about the analytics on time scales. For further details on time scale analysis, we refer the reader to the excellent monograph by Bohner [36] which summarizes and organizes much of the time scale calculus. Next, some essential lemmas on time scales, which will be needed in the proofs of the presented paper, are listed.…”

Section: Basic Concepts and Lemmas On Time Scalesmentioning

confidence: 99%

“…Following the same steps from (29)- (33) with suitable changes and substituting (25), (34), (36) in 35, we have…”

Section: Theorem 37mentioning

confidence: 99%

Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications

Khan

2019

Bound Value Probl

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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. 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.

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“…21, Theorem 1.90]. The section on the geometric sense of differentiability is extracted from Bohner and Guseinov[8]. Throughout the book, results are given in terms of delta derivatives, but all results may also be formulated with nabla instead.…”

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confidence: 99%