scholarly journals Lacunary statistical boundedness on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bayram Sözbir ◽  
Selma Altundağ
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Arbitrary Time ◽  
Statistical Boundedness

AbstractIn this paper, we introduce the concept of lacunary statistical boundedness of Δ-measurable real-valued functions on an arbitrary time scale. We also give the relations between statistical boundedness and lacunary statistical boundedness on time scales.

Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Xin Wu ◽  
Taixiang Sun
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Time Scale ◽  
Higher Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Arbitrary Time ◽  
Delay Dynamic Equation ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

AbstractIn this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equationon an arbitrary time scalewith

scholarly journals Lyapunov-Type Inequalities for Some Quasilinear Dynamic System Involving the(p1,p2,…,pm)-Laplacian on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Xiaofei He ◽  
Qi-Ming Zhang
Keyword(s):  
Dynamic System ◽  
Time Scales ◽  
Time Scale ◽  
Arbitrary Time

We establish several new Lyapunov-type inequalities for some quasilinear dynamic system involving the(p1,p2,…,pm)-Laplacian on an arbitrary time scale𝕋, which generalize and improve some related existing results including the continuous and discrete cases.

Local-periodic solutions for functional dynamic equations with infinite delay on changing-periodic time scales

2018 ◽  
Vol 68 (6) ◽  
pp. 1397-1420 ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Time Scale ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Arbitrary Time ◽  
First Time ◽  
Composition Theorem

Abstract In this paper, by using the concept of changing-periodic time scales and composition theorem of time scales introduced in 2015, we establish a local phase space for functional dynamic equations with infinite delay (FDEID) on an arbitrary time scale with a bounded graininess function μ. Through Krasnoseľskiĭ’s fixed point theorem, some sufficient conditions for the existence of local-periodic solutions for FDEID are established for the first time. This research indicates that one can extract a local-periodic solution for dynamic equations on an arbitrary time scale with a bounded graininess function μ through some index function.

scholarly journals The exponential of a constant matrix on time scales

2006 ◽  
Vol 48 (1) ◽  
pp. 99-106 ◽  
Author(s):  
A. Zafer
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Matrix Exponential ◽  
Constant Matrix ◽  
Arbitrary Time ◽  
Elementary Method ◽  
The Matrix

AbstractIn this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result.

scholarly journals Uniform Statistical Convergence on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yavuz Altin ◽  
Hikmet Koyunbakan ◽  
Emrah Yilmaz
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Statistical Convergence ◽  
Uniform Density ◽  
Cauchy Function ◽  
Arbitrary Time

We will introduce the concept ofm- and(λ,m)-uniform density of a set andm- and(λ,m)-uniform statistical convergence on an arbitrary time scale. However, we will definem-uniform Cauchy function on a time scale. Furthermore, some relations about these new notions are also obtained.

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

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zareen A. Khan
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Unknown Function ◽  
Nonlinear Dynamic ◽  
Time Interval ◽  
Specific Class ◽  
Initial Condition ◽  
Basic Technique ◽  
Arbitrary Time ◽  
Independent Variable

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 $\mathbb{T}$ 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.

scholarly journals Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Hardy Type Inequalities ◽  
Arbitrary Time ◽  
Hardy Type ◽  
Several Variables ◽  
New Inequalities

We extend some Hardy-type inequalities with general kernels to arbitrary time scales using multivariable convex functions. Some classical and new inequalities are deduced seeking applications.

Wirtinger's Inequalities on Time Scales

2008 ◽  
Vol 51 (2) ◽  
pp. 161-171 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Victoria Otero-Espinar ◽  
Kanishka Perera ◽  
Dolores R. Vivero
Keyword(s):  
Continuous Function ◽  
Time Scales ◽  
Time Scale ◽  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
General Inequality ◽  
Arbitrary Time ◽  
Absolutely Continuous Function

AbstractThis paper is devoted to the study of Wirtinger-type inequalities for the Lebesgue Δ-integral on an arbitrary time scale 𝕋. We prove a general inequality for a class of absolutely continuous functions on closed subintervals of an adequate subset of 𝕋. By using this expression and by assuming that 𝕋 is bounded, we deduce that a general inequality is valid for every absolutely continuous function on 𝕋 such that its Δ-derivative belongs to([a,b) ∩ 𝕋) and at most it vanishes on the boundary of 𝕋.

scholarly journals SOME CLASSES OF CONVEX FUNCTIONS ON TIME SCALES

2020 ◽  
Vol 35 (1) ◽  
pp. 011
Author(s):  
Fagbemigun Opeyemi Bosede ◽  
Adesanmi A. Mogbademu
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Arbitrary Time ◽  
New Concepts

We have introduced diamond $\phi_{h-s, \mathbb{T}}$ derivative and diamond $\phi_{h-s,\mathbb{T}}$ integral on an arbitrary time scale. Moreover, various interconnections with the notion of classes of convex functions about these new concepts are also discussed.

scholarly journals Some inequalities of Ostrowski and Grüss type for triple integrals on time scales

2011 ◽  
Vol 42 (4) ◽  
pp. 415-426 ◽  
Author(s):  
Nazir Ahmad Mir ◽  
Roman Ullah
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Partial Derivatives ◽  
Arbitrary Time ◽  
Grüss Type Inequalities

In this paper, we establish some inequalities of Ostrowski and Grüss type for triple integrals on arbitrary time scales involving three functions and their partial derivatives. We also discuss the discrete Ostrowski and Grüss type inequalities for triple sumon time scale.

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