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On statistical convergence and strong Cesaro convergence by moduli for double sequences

JOURNAL OF INEQUALITIES AND APPLICATIONS 2022年第1期2022卷 1-14页

作者： Leon-Saavedra, Fernando Del Carmen Listan-Garcia, Maria Romero de la Rosa, Maria del Pilar Univ Cadiz Dept Math Avda Univ S-N Jerez de la Frontera 11405 Spain Univ Cadiz Fac Ciencias Dept Math Puerto Real 11510 Spain

A remarkable result on summability states that the statistical convergence and the strong Cesaro convergence are closely connected. Given a modulus function f, we will establish that a double sequence that is f-strong Cesaro convergent is always f-statistically convergent. The converse, in general, is false even for bounded sequences. However, we will characterize analytically the modulus functions f for which the converse of this result remains true. The results of this paper adapt to several variables the results obtained in (Leon-Saavedra et al. in J. Inequal. Appl. 12:298, 2019).

关键词： Statistical convergence Double sequences Strong Cesaro convergence modulus function

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Deferred (formula presented, f) -Statistical Convergence of Order a in Normed Space 5th

Deferred (formula presented, f) -Statistical Convergence of...

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5th International Conference On Mathematical Modelling, Applied Analysis And Computation, ICMMAAC 2022

作者： Verma, A.K. Kumar, Sudhanshu Dr. Harisingh Gour Vishwavidyalaya M.P. Sagar470003 India

ISBN: (纸本)9783031299582

In this paper, we introduced the space of all deferred -statistically convergent sequences of order in the normed space (X, q) with the help of generalized difference operator unbounded modulus function f, and deferred sequences of non-negative integers with or any We also introduced the space of all strongly deferred summable sequences of order in the normed space (X, q). Inclusion relations between spaces and are established under certain conditions. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Deferred sequences Difference sequence space modulus function Statistical convergence

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Generalized Hermite-Hadamard type inequalities for generalized F-convex function via local fractional integrals

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CHAOS SOLITONS & FRACTALS 2023年第1期168卷

作者： Razzaq, Arslan Rasheed, Tahir Shaokat, Shahid Comsats Univ Islamabad Lahore Campus Islamabad Pakistan

In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets R �� (0 < ��& LE;1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite-Hadamard type inequalities in the fractals sense. In this work, we present some new results by employing local fractional calculus for twice differentiable functions along with some new definitions. For the development of these new integral inequalities, we will use generalized Hilder-integral inequality and power mean integral inequality by using local fractional calculus. Moreover, we give some new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works.

关键词： Convex functions Hermite-Hadamard inequality modulus function Hilder's inequality Power mean inequality

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On asymptotically statistical equivalent functions on time scales

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2022年第18期45卷 12099-12109页

作者： Sozbir, Bayram Altundag, Selma Sakarya Univ Arts & Sci Fac Dept Math Sakarya Turkey

In this paper, we introduce the concepts of asymptotically f-statistical equivalence, asymptotically f-lacunary statistical equivalence, and strong asymptotically f-lacunary equivalence for non-negative two delta measurable real-valued functions defined on time scales with the aid of modulus function f. Furthermore, the relationships between these new concepts are investigated. We also present some inclusion theorems.

关键词： asymptotical equivalent functions delta measure on time scale lacunary statistical convergence modulus function statistical convergence time scale

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An analytical model for the interaction between two dissimilar piles in a finite soil layer

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2021年第7期45卷 950-964页

作者： Liu, Huan Liu, Qijian Hunan Univ Coll Civil Engn Changsha Hunan Peoples R China Hunan Univ Minist Educ Key Lab Bldg Safety & Energy Efficiency Changsha Hunan Peoples R China

An analytical method is developed for the interaction between two dissimilar piles subjected to vertical loadings in a finite soil layer with a rigid base. A fictitious soil column is assumed for the corresponding shaft and the moduli of the soil-pile rod are expressed as a Heaviside step function of the modulus. The vertical soil displacements and the shaft resistances are calculated as the combined contributions by the two dissimilar piles in terms of the respective local coordinate systems. The displacements and stresses in two different local coordinates are transferred from one to the other using Graf's addition theorem. The boundary value problem for the soil layer is solved using the method of separation of variables with a series of undetermined constants. The unknown constants can be determined by considering the compatibility along the interfaces of the two soil-pile rods and the surrounding soil. A parametric study is performed to investigate the effects of the properties of the soil-pile system on the interaction between the two piles. Numerical results show that, for the dissimilar piles in the stiff soil, the effects of the difference of the pile lengths on the interaction factor are negligible. Also, the interaction factor of the dissimilar piles in the soft soil depends heavily on the difference in lengths.

关键词： dissimilar piles Graf's addition theorem interaction factor modulus function vertical loadings

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df-statistical convergence in connection with a modulus in metric spaces

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第10期50卷 2270-2280页

作者： Kayan, Emine Colak, Rifat Firat Univ Dept Math TR-23119 Elazig Turkey

In this study we introduce -statistical convergence and -strong Cesaro summability with respect to a modulus for a sequence in a metric space. Furthermore we give the relations between the set of -statistically convergent sequences and the set of -strongly Cesaro summable sequences with respect to a modulus. Besides this we give the relations between the set of -strongly Cesaro summable and the set of -strongly Cesaro summable sequences in connection with a modulus.

关键词： density modulus function statistical convergence strong Cesaro summability

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Applications of deferred Cesaro statistical convergence of sequences of fuzzy numbers of order (ξ, ω)

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第6期41卷 7363-7372页

作者： Sharma, Sonali Singh, Uday Pratap Raj, Kuldip Shri Mata Vaishno Devi Univ Sch Math Katra Jammu & Kashmir India

The purpose of this article is to study deferred Cesrao statistical convergence of order (xi, omega) associated with a modulus function involving the concept of difference sequences of fuzzy numbers. The study reveals that the statistical convergence of these newly formed sequence spaces behave well for xi = omega. and convergence is not possible for xi > omega. We also define p-deferred Cesaro summability and establish several interesting results. In addition, we provide some examples which explain the validity of the theoretical results and the effectiveness of constructed sequence spaces. Finally, with the help of MATLAB software, we examine that if the sequence of fuzzy numbers is bounded and deferred Cesaro statistical convergent of order (xi, omega) in (Delta, F, f), then it need not be strongly p-deferred Cesaro summable of order (xi, omega) in general for 0 < xi <= omega <= 1.

关键词： Statistical convergence fuzzy sequence deferred Cesaro mean modulus function difference sequence space

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On generalized invariant statistical convergence of weight g

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第8期50卷 1699-1708页

作者： Savas, Ekrem Usak Univ Math TR-64200 Usak Turkey

The goal of this paper is to introduce the concept of lambda-invariant statistical convergence of weight where for any sequence in with We also investigate some relations between lambda-invariant statistical convergence of weight g and strong -summability of weight g and then the relations between the spaces and then the relations between the spaces and.

关键词： Cesaro summability invariant convergence modulus function statistical convergence weight function g

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Modelling edge effects at the interface in bonded joints using gradient functions in the mechanical properties of the adhesive: Application of the method to the Arcan test loaded in tension and shear

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INTERNATIONAL JOURNAL OF ADHESION AND ADHESIVES 2023年 120卷

作者： Benali, A. Cellard, C. Sohier, L. Moretti, A. Creachcadec, R. ENSTA Bretagne IRDL UMR CNRS 6027 Brest France Univ Bretagne Occidentale IRDL UMR CNRS 6027 Brest France EXCELCAR Ty PoC Chartres de Bretagne France Engn Concept Maintenance Paris France

The design of bonded joints requires studies of stress concentrations due to edge effects. For complex joint configurations, the finite element method can be quite costly. The objective is to develop a fast and reliable numerical design tool for bonded assemblies. Therefore, an approach to design bonded assemblies is presented which aims to meet the needs of a design office, particularly in terms of calculation costs. The latter consists in reproducing the edge effects with a single element through the joint thickness using a modulus function. The concept was tested on Arcan specimen with two loading cases: tension (gamma = 0 degrees) and shear (gamma = 90 degrees). A 2D model under the elastic assumption is developed to describe the edge effects of the joint using Abaqus subroutines (UMat). The approach is set up to solve this problem in the form of two blocks. First, mesh refinement studies for bonded specimens loaded in tension were performed, within a good level of accuracy, on the free edge with the use of local discretization error estimation. After that, the effects of local geometry and modulus ratio are investigated. Afterwards, the von Mises stress at the interface level of the adhesive joint was used to identify a modulus function to describe the behavior of a joint with straight edge geometry for tension and shear loadings. The proposed approach has improved the performance of the model. Actually, the calculation is practically three times faster than for the conventional model.

关键词： Bonded joint design Edge effects modulus function Computational cost

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Convergence of measurable functions in the sense of density

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JOURNAL OF ANALYSIS 2023年第2期31卷 1487-1510页

作者： Altinok, Maya Kucukaslan, Mehmet Unay, A. Kerem Tarsus Univ Dept Nat & Math Sci TR-33400 Tarsus Mersin Turkey Mersin Univ Dept Math TR-33343 Mersin Turkey

In this paper, by using unbounded modulus function the notion mu(f)-density for measurable subsets of I = [1, infinity] is defined and related notion mu f-statistical convergence of measurable functions is investigated. In addition to the basic properties of mu(f)-density and mu(f)-statistical convergence, the definition of being mu(f)-Cauchy is given and it is shown that these two concepts are equivalent for real valued measurable functions. Among others, the notion of f-strongly Cesaro summability is introduced. Finally, necessary and sufficient conditions between f-strongly Cesaro summability and mu(f)-statistical convergence are given under explicated restrictions on measurable function and modulus function.

关键词： Convergence Statistical convergence Measurable functions modulus function

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