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Statistical Convergence of order β for (λ, ,μ) double sequences of fuzzy numbers

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020年第5期39卷 6949-6954页

作者： Barlak, Damla Dicle Univ Dept Stat Diyarbakir Turkey

In this study, we introduce the concepts of phi(lambda,mu)-double statistically convergence of order beta in fuzzy sequences and strongly lambda- double Cesaro summable of order beta for sequences of fuzzy numbers. Al... 详细信息

关键词： Statistical convergence Cesaro summability modulus function

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An Improved Steganography Method Based on Least-Significant-Bit Substitution and Pixel-Value Differencing

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KSII TRANSACTIONS ON INTERNET AND INFORMATION SYSTEMS 2020年第11期14卷 4537-4556页

作者： Liu, Hsing-Han Su, Pin-Chang Hsu, Meng-Hua Natl Def Univ Dept Informat Management 70Sec 2Zhongyang N Rd Taipei 112 Taiwan

This research was based on the study conducted by Khodaei et al. (2012), namely, the least significant-bit (LSB) substitution combined with the pixel-value differencing (PVD) steganography, and presented an improved irreversible image steganography method. Such a method was developed through integrating the improved LSB substitution with the modulus function-based PVD steganography to increase steganographic capacity of the original technique while maintaining the quality of images. It partitions the cover image into non overlapped blocks, each of which consists of 3 consecutive pixels. The 2nd pixel represents the base, in which secret data are embedded by using the 3-bit LSB substitution. Each of the other 2 pixels is paired with the base respectively for embedding secret data by using an improved modulus PVD method. The experiment results showed that the method can greatly increase steganographic capacity in comparison with other PVD-based techniques (by a maximum amount of 135%), on the premise that the quality of images is maintained. Last but not least, 2 security analyses, the pixel difference histogram (PDH) and the content selective residual (CSR) steganalysis were performed. The results indicated that the method is capable of preventing the detection of the 2 common techniques.

关键词： Steganography irreversible least-significant-bit pixel-value differencing modulus function

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Applications of Fibonacci matrix to characterize some Banach spaces through weakly unconditional Cauchy series

ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS

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ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2022年第48期48卷 1049-1059页

作者： Raj, Kuldip Choudhary, Anu Aiyub, M. Sharma, Sonali Shri Mata Vaishno Devi Univ Dept Math Katra 182320 Jammu & Kashmir India Univ Bahrain Coll Sci Dept Math Manam Bahrain

In this article, we introduce new sequence spaces U(T(x), F, p, u), U(Tw(x), F, p, u) and U(Tw*(h), F, p, u) by using Fibonacci matrix and sequence of modulus func-tions. We make an effort to study some characterizations of weakly unconditionally Cauchy series associated to newly formed sequence spaces. Finally, the barreledness of a normed space Y is characterized by means of weakly* unconditionally Cauchy series in Y*.

关键词： modulus function weakly unconditionally Cauchy series Fibonacci se-quence spaces barreledness

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Improving the Adaptive Steganographic Methods Based on modulus function

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2013年第12期E96A卷 2731-2734页

作者： Liao, Xin Wen, Qiaoyan Zhang, Jie Hunan Univ Coll Informat Sci & Engn Changsha 410082 Hunan Peoples R China Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China

This letter improves two adaptive steganographic methods in Refs. [5], [6], which utilize the remainders of two consecutive pixels to record the information of secret data. Through analysis, we point out that they perform mistakenly under some conditions, and the recipient cannot extract the secret data exactly. We correct these by enlarging the adjusting range of the remainders of two consecutive pixels within the block in the embedding procedure. Furthermore, the readjusting phase in Ref. [6] is improved by allowing every two-pixel block to be fully modified, and then the sender can select the best choice that introduces the smallest embedding distortion. Experimental results show that the improved method not only extracts secret data exactly but also reduces the embedding distortion.

关键词： steganography adaptive steganographic methods pixel-value differencing modulus function

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Some Relations Between the Sets of f-Statistically Convergent Sequences 4th

Some Relations Between the Sets of f-Statistically Convergen...

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4th International Conference on Computational Mathematics and Engineering Sciences (CMES)

作者： Colak, Rifat Firat Univ Dept Math Elazig Turkey

ISBN: (纸本)9783030391126;9783030391119

In this study we first established the relations between f-density and g-density of a subset of the set of positive integers for any modulus functions f and g. Using the obtained facts we establish the relationship between the sets S-f and S-g of statistically convergent and BSf and BSg of statistically bounded sequences which defined by modulus functions f and g.

关键词： Density modulus function Statistical convergence Statistical boundedness

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Generalized lacunary Δ^m-statistically convergent sequences of fuzzy numbers using a modulus function

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Journal of Inequalities and Applications 2013年第1期2013卷 1-13页

作者： Srivastava, Parmeshwary Dayal Mohanta, Sushomita Department of Mathematics Indian Institute of Technology Kharagpur 721302 India

In this paper, we introduce the space of lacunary strongly Δ(p)m-summable sequences of fuzzy numbers and discuss relations between Δm-statistically convergent sequences and lacunary Δm-statistically convergent sequ... 详细信息

In this paper, we introduce the space of lacunary strongly Δ_(p)^m-summable sequences of fuzzy numbers and discuss relations between Δ^m-statistically convergent sequences and lacunary Δ^m-statistically convergent sequences of fuzzy numbers. We also study inclusion relations using different arbitrary lacunary sequences. ©2013 Srivastava and Mohanta;licensee Springer.

关键词： Fuzzy number Lacunary Δm-statistical convergence Lacunary refinement modulus function

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Lacunary statistical convergence of order α,β for generalized vector-valued difference sequence spaces

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JOURNAL OF ANALYSIS 2020年第3期28卷 711-726页

作者： Verma, A. K. Kumar, Sudhanshu Dr HS Gour Cent Univ Dept Math & Stat Sagar 470003 Madhya Pradesh India

In this paper, we defined space S theta alpha,beta(Delta vm,E,q) of all vector-valued lacunary Delta vm-statistical convergent sequences of order (alpha,beta) and space N theta alpha,beta(Delta vm,E,q,p) of all vector-valued strongly Delta vm-lacunary summable sequences of order (alpha,beta) by taking sequence (Ek,qk) of normed spaces, where p is a positive real number and alpha,beta are real numbers with 0<beta 1. Some inclusion relations between these spaces are obtained. We also studied space omega theta alpha,beta(Delta vm,f,E,q,p) of all vector-valued strongly Delta vm-lacunary summable sequences of order (alpha,beta) with respect to modulus function f by taking a bounded sequence (pk) of strictly positive real numbers with infkpk>0. The inclusion relations between spaces omega theta alpha,beta(Delta vm,f,E,q,p) and S theta alpha,beta(Delta vm,E,q) are determined.

关键词： Statistical convergence Lacunary sequence Difference sequence space Paranormed space modulus function Statistical convergence-40A35 Difference sequence space-40C05 Paranormed space-46E99

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Generating new ideals using weighted density via modulus functions

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INDAGATIONES MATHEMATICAE-NEW SERIES 2018年第5期29卷 1196-1209页

作者： Bose, Kumardipta Das, Pratulananda Kwela, Adam Jadavpur Univ Dept Math Kolkata 700032 India Univ Gdansk Inst Math Fac Math Phys & Informat Ul Wita Stwosza 57 PL-80308 Gdansk Poland

In this paper we extend the idea of weighted density of Balcerzak et al. (2015) by using a modulus function and introduce the idea f -density of weight g of subsets of omega := {0,1, ...} (at the same time extending the notion of f-density (Aizpuru et al., 2014)), which we name d(g)(f) where g : omega -> [0, infinity) satisfies g(n) -> infinity and n/g(n) -> 0 and f is a modulus function. The aim of this paper is to show that we can get new ideals Z(g)(f) consisting of sets A subset of omega co for which d(g)(f) (A) = 0 different from all the previously constructed ideals Z(g) (f) of Balcerzak et al. (2015) and moreover they retain all the nice properties of the ideals Z(g). (C) 2018 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

关键词： Generalized density Weight function modulus function P-ideal Density ideal Borel complexity

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Statistical Convergence of Order 4th

Statistical Convergence of Order

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4th International Conference on Computational Mathematics and Engineering Sciences, CMES 2019

作者： Savaş, Ekrem Department of Mathematics Uşak University Uşak Turkey

In this paper we introduce - statistically convergent of order. In addition, we establish some connections between - statistically convergent of order and the – strong convergence of order". © 2020, Springe... 详细信息

ISBN: (纸本)9783030391119

关键词： function Matrix transformations modulus function Statistically convergent of order

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(Δ^m, f) - Statistical convergence for sequences of fuzzy numbers

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019年第4期36卷 3525-3533页

作者： Altinok, Hifsi Deniz, Derya Firat Univ Dept Math TR-23119 Elazig Turkey

In this paper, we define the concepts of (Delta(m), f)-statistical convergence of order ss and strong (Delta(m), f)-Cesaro summability of order beta for beta is an element of (0, 1] using a generalized difference operator Delta(m) and an unbounded modulus function for sequences of fuzzy numbers and give some inclusion relations between them.

关键词： Sequence of fuzzy numbers difference operator statistical convergence Cesaro summability modulus function

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