Fundamental properties of statistical convergence and lacunary statistical convergence on time scales

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4455-4467 ◽  
Author(s):  
Ceylan Turan ◽  
Oktay Duman
Keyword(s):  
Time Scales ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Tauberian Condition ◽  
Fundamental Properties ◽  
Lacunary Statistical Convergence ◽  
Necessary And Sufficient

In this paper, we first obtain a Tauberian condition for statistical convergence on time scales. We also find necessary and sufficient conditions for the equivalence of statistical convergence and lacunary statistical convergence on time scales. Some significant applications are also presented.

Semi-invariant submanifolds of a normal almost paracontact manifold

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4875-4887 ◽  
Author(s):  
Mehmet Atçeken ◽  
Siraj Uddin
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fundamental Properties ◽  
Invariant Submanifolds ◽  
Normal Almost Paracontact Manifold ◽  
Necessary And Sufficient

In this paper, we introduce the notion of semi-invariant submanifolds of a normal almost paracontact manifold. We study their fundamental properties and the particular cases. The necessary and sufficient conditions are given for a submanifold to be invariant or anti-invariant. Also, we give some results for semi-invariant submanifolds of a normal almost paracontact manifold with constant c and we construct an example.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

scholarly journals Stability Criteria for Volterra Integrodynamic System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Nusrat Yasmin ◽  
Awais Younus ◽  
Usman Ali ◽  
Safia Mirza
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Qualitative Behavior ◽  
Lyapunov Functionals ◽  
Stability Criteria ◽  
Necessary And Sufficient

We study conditions under which the solutions of linear Volterra integrodynamic system of the formyΔt=Atyt+∫t0tKt,sysΔsare stable on certain time scales. We construct a number of Lyapunov functionals on time scales from which we obtain necessary and sufficient conditions for stability of Volterra integrodynamic system and also we prove several results concerning qualitative behavior of this system.

scholarly journals Tauberian conditions under which statistical convergence follows from statistical summability $(EC)_{n}^1$

2018 ◽  
Vol 37 (4) ◽  
pp. 9
Author(s):  
Naim L. Braha ◽  
Ismet Temaj
Keyword(s):  
Finite Number ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complex Numbers ◽  
Real Numbers ◽  
Tauberian Conditions ◽  
Necessary And Sufficient

Let $(x_k)$, for $k\in \mathbb{N}\cup \{0\}$  be a sequence of real or complex numbers and set $(EC)_{n}^{1}=\frac{1}{2^n}\sum_{j=0}^{n}{\binom{n}{j}\frac{1}{j+1}\sum_{v=0}^{j}{x_v}},$ $n\in \mathbb{N}\cup \{0\}.$  We present necessary and sufficient conditions, under which $st-\lim_{}{x_k}= L$ follows from $st-\lim_{}{(EC)_{n}^{1}} = L,$ where L is a finite number. If $(x_k)$ is a sequence of real numbers, then these are one-sided Tauberian conditions. If $(x_k)$ is a sequence of complex numbers, then these are two-sided Tauberian conditions.

scholarly journals Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces

2018 ◽  
Vol 38 (1) ◽  
pp. 117-129
Author(s):  
Mausumi Sen ◽  
Mikail Et
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Sufficient Conditions ◽  
Inclusion Relation ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Difference Sequences ◽  
Lacunary Statistical Convergence ◽  
Necessary And Sufficient

In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence of generalized difference sequences have been established. The notion of strong Cesaro summability in intuitionistic fuzzy normed linear spaces has been introduced and studied. Also the concept of lacunary generalized difference statistically Cauchy sequence has been introduced and some results are established.

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