Pub Date : 2019-10-15DOI: 10.36753/MATHENOT.597703
M. İlkhan, P. Alp
In this study, we introduce a new matrix $hat{T}^q=(hat{t}^q_{nk})$ by [ hat{t}^q_{nk}=left { begin{array} [c]{ccl}% frac{q_n}{Q_n} t_n & , & k=n frac{q_k}{Q_n}t_k-frac{q_{k+1}}{Q_n} frac{1}{t_{k+1}} & , & k n . end{array} right. ] where $t_k>0$ for all $ninmathbb{N}$ and $(t_n)in cbackslash c_0$ . By using the matrix $hat{T}^q$ , we introduce the sequence space $ell_p(hat{T}^q)$ for $1leq pleqinfty$ . In addition, we give some theorems on inclusion relations associated with $ell_p(hat{T}^q)$ and find the $alpha$ -, $beta$ -, $gamma$ - duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes $(ell_p(hat{T}^q),lambda)$ or $(lambda,ell_p(hat{T}^q))$ , where $lambdain{ell_1,c_0,c,ell_infty}$ .
{"title":"On The Difference Sequence Space $l_p(hat{T}^q)$","authors":"M. İlkhan, P. Alp","doi":"10.36753/MATHENOT.597703","DOIUrl":"https://doi.org/10.36753/MATHENOT.597703","url":null,"abstract":"In this study, we introduce a new matrix $hat{T}^q=(hat{t}^q_{nk})$ by [ hat{t}^q_{nk}=left { begin{array} [c]{ccl}% frac{q_n}{Q_n} t_n & , & k=n frac{q_k}{Q_n}t_k-frac{q_{k+1}}{Q_n} frac{1}{t_{k+1}} & , & k n . end{array} right. ] where $t_k>0$ for all $ninmathbb{N}$ and $(t_n)in cbackslash c_0$ . By using the matrix $hat{T}^q$ , we introduce the sequence space $ell_p(hat{T}^q)$ for $1leq pleqinfty$ . In addition, we give some theorems on inclusion relations associated with $ell_p(hat{T}^q)$ and find the $alpha$ -, $beta$ -, $gamma$ - duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes $(ell_p(hat{T}^q),lambda)$ or $(lambda,ell_p(hat{T}^q))$ , where $lambdain{ell_1,c_0,c,ell_infty}$ .","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133681050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-10DOI: 10.36753/mathenot.683046
C. Unal
We consider several fundamental properties of grand variable exponent Lebesgue spaces. Moreover, we discuss Ergodic theorems in these spaces whenever the exponent is invariant under the transformation.
讨论了大变指数勒贝格空间的几个基本性质。此外，我们还讨论了指数在变换下不变时的遍历定理。
{"title":"Ergodic Theorem in Grand Variable Exponent Lebesgue Spaces","authors":"C. Unal","doi":"10.36753/mathenot.683046","DOIUrl":"https://doi.org/10.36753/mathenot.683046","url":null,"abstract":"We consider several fundamental properties of grand variable exponent Lebesgue spaces. Moreover, we discuss Ergodic theorems in these spaces whenever the exponent is invariant under the transformation.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":" 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132012208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/mathenot.559244
Said Baghdad, M. Benchohra
In this paper we provide sufficient condition guaranteeing existence and the asymptotic behavior of solutions of a class of Hadamard–Volterra integral equations in the Banach space of continuous and bounded functions on unbounded interval. The main tools used in our considerations are the concept of measure of noncompactness in conjunction with the Darbo and Monch fixed point theorems.
{"title":"On Existence and Asymptotic Behavior of Solutions of Hadamard-Volterra Integral Equations","authors":"Said Baghdad, M. Benchohra","doi":"10.36753/mathenot.559244","DOIUrl":"https://doi.org/10.36753/mathenot.559244","url":null,"abstract":"In this paper we provide sufficient condition guaranteeing existence and the asymptotic behavior of solutions of a class of Hadamard–Volterra integral equations in the Banach space of continuous and bounded functions on unbounded interval. The main tools used in our considerations are the concept of measure of noncompactness in conjunction with the Darbo and Monch fixed point theorems.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128945428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/MATHENOT.559241
Zlatko Pavić
The paper deals with discrete forms of double inequalities related to convex functions of one variable. Infinite convex combinations and sequences of convex combinations are included. The double inequality form of the Jensen-Mercer inequality and its variants are especially studied.
{"title":"The Jensen-Mercer Inequality with Infinite Convex Combinations","authors":"Zlatko Pavić","doi":"10.36753/MATHENOT.559241","DOIUrl":"https://doi.org/10.36753/MATHENOT.559241","url":null,"abstract":"The paper deals with discrete forms of double inequalities related to convex functions of one variable. Infinite convex combinations and sequences of convex combinations are included. The double inequality form of the Jensen-Mercer inequality and its variants are especially studied.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115285961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/MATHENOT.559255
B. Venkateswarlu, M. Rao, Y. A. Narayana
In this paper, we introduce the notion of reverse derivation and orthogonal reverse derivations on Γ-semirings. Some characterizations of semi prime Γ-semirings are obtained by means of orthogonal reverse derivations. And also obtained necessary and sufficient conditions for two reverse derivations to be orthogonal.
{"title":"Orthogonal Reverse Derivations on semiprime Γ-semirings","authors":"B. Venkateswarlu, M. Rao, Y. A. Narayana","doi":"10.36753/MATHENOT.559255","DOIUrl":"https://doi.org/10.36753/MATHENOT.559255","url":null,"abstract":"In this paper, we introduce the notion of reverse derivation and orthogonal reverse derivations on Γ-semirings. Some characterizations of semi prime Γ-semirings are obtained by means of orthogonal reverse derivations. And also obtained necessary and sufficient conditions for two reverse derivations to be orthogonal.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122708828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/mathenot.559265
O. Kharazmi, Ali Saadatinik, M. Tamandi
Kharazmi and Saadatinik [21] introduced a new family of distribution called hyperbolic cosine – F (HCF) distributions. They studied some properties of this model and obtained the estimates of its parameters by different methods. In this paper, it is focused on a special case of HCF family withWeibull distribution as a baseline model. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropies are derived. Superiority of this model is proved in some simulations and applications.
Kharazmi和Saadatinik[21]引入了一种新的分布族，称为双曲余弦- F (HCF)分布。他们研究了该模型的一些性质，并通过不同的方法得到了其参数的估计。本文主要研究以威布尔分布为基准模型的HCF族的一种特殊情况。推导了该分布的各种性质，包括矩的显式表达式、分位数、矩生成函数、故障率函数、平均残差寿命、序统计量和熵的表达式。仿真和实际应用证明了该模型的优越性。
{"title":"A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets","authors":"O. Kharazmi, Ali Saadatinik, M. Tamandi","doi":"10.36753/mathenot.559265","DOIUrl":"https://doi.org/10.36753/mathenot.559265","url":null,"abstract":"Kharazmi and Saadatinik [21] introduced a new family of distribution called hyperbolic cosine – F (HCF) distributions. They studied some properties of this model and obtained the estimates of its parameters by different methods. In this paper, it is focused on a special case of HCF family withWeibull distribution as a baseline model. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropies are derived. Superiority of this model is proved in some simulations and applications.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"217 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132979711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/MATHENOT.521075
M. Kulahci, M. Bektaş, A. Bilici
This study provides the de…nition of rectifying, normal and osculating curves in 3-dimensional Sasakian space with their characterizations. Furthermore, the di¤erential equations obtained from these characterizations are solved and their figures are presented in the text.
{"title":"On Classifications of Normal and Osculating Curves in 3-dimensional Sasakian Space","authors":"M. Kulahci, M. Bektaş, A. Bilici","doi":"10.36753/MATHENOT.521075","DOIUrl":"https://doi.org/10.36753/MATHENOT.521075","url":null,"abstract":"This study provides the de…nition of rectifying, normal and osculating curves in 3-dimensional Sasakian space with their characterizations. Furthermore, the di¤erential equations obtained from these characterizations are solved and their figures are presented in the text.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122393371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/MATHENOT.559260
Y. Cengellenmis, A. Dertli
In this paper, the quantum codes over F q are constructed by using the cyclic codes over the finite ring R = F q + vF q + ... + v m − 1 F q , where p is prime, q = p s , m − 1 | p − 1 and v m = v . The parameters of quantum error correcting codes over F q are obtained. Some examples are given. Morever, the quantum quasi-cyclic codes over F p are obtained, by using the self dual basis for F p s over F p .
本文利用有限环R = F q + vF q +…上的循环码构造了F q上的量子码。+ v m−1 F q，其中p为素数，q = p s m−1 | p−1 v m = v。得到了fq上的量子纠错码的参数。给出了一些例子。利用F / p的自对偶基，得到了F / p上的量子拟循环码。
{"title":"The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p","authors":"Y. Cengellenmis, A. Dertli","doi":"10.36753/MATHENOT.559260","DOIUrl":"https://doi.org/10.36753/MATHENOT.559260","url":null,"abstract":"In this paper, the quantum codes over F q are constructed by using the cyclic codes over the finite ring R = F q + vF q + ... + v m − 1 F q , where p is prime, q = p s , m − 1 | p − 1 and v m = v . The parameters of quantum error correcting codes over F q are obtained. Some examples are given. Morever, the quantum quasi-cyclic codes over F p are obtained, by using the self dual basis for F p s over F p .","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115973152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-30DOI: 10.36753/mathenot.559247
H. Kadakal, I. Işcan
In this study, a new identity for functions defined on an open invex subset of set of real numbers is formed. After that we established Hermite-Hadamard-like inequalities for this type of functions. Then, by using the this identity and the Holder and Power mean integral inequalities we present new type integral inequalities for functions whose powers of fourth derivatives in absolute value are preinvex functions.
{"title":"New Inequalities for Preinvex Functions","authors":"H. Kadakal, I. Işcan","doi":"10.36753/mathenot.559247","DOIUrl":"https://doi.org/10.36753/mathenot.559247","url":null,"abstract":"In this study, a new identity for functions defined on an open invex subset of set of real numbers is formed. After that we established Hermite-Hadamard-like inequalities for this type of functions. Then, by using the this identity and the Holder and Power mean integral inequalities we present new type integral inequalities for functions whose powers of fourth derivatives in absolute value are preinvex functions.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123948090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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