: This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.
{"title":"Oscillation of second order difference equation with a sub-linear neutral term","authors":"C. Dharuman, J. Graef, E. Thandapani, K. Vidhyaa","doi":"10.7862/RF.2017.4","DOIUrl":"https://doi.org/10.7862/RF.2017.4","url":null,"abstract":": This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124814589","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}
{"title":"On the Maximum Modulus of a Polynomial","authors":"V. K. Jain","doi":"10.7862/rf.2019.7","DOIUrl":"https://doi.org/10.7862/rf.2019.7","url":null,"abstract":"","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121642204","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}
The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok- Srivastava operator. We further investigate convolution properties for these calsses. We also nd necessary and sucient
{"title":"Convolution properties of subclasses of analytic functions associated with the Dziok-Srivastava operator","authors":"S. Goyal, S. Bansal, P. Goswami, Zhi-Gang Wang","doi":"10.7862/RF.2013.6","DOIUrl":"https://doi.org/10.7862/RF.2013.6","url":null,"abstract":"The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok- Srivastava operator. We further investigate convolution properties for these calsses. We also nd necessary and sucient","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124150635","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}
A method of the finite approximation of continuous noncooperative two-person games is presented. The method is based on sampling the functional spaces, which serve as the sets of pure strategies of the players. The pure strategy is a linear function of time, in which the trenddefining coefficient is variable. The spaces of the players’ pure strategies are sampled uniformly so that the resulting finite game is a bimatrix game whose payoff matrices are square. The approximation procedure starts with not a great number of intervals. Then this number is gradually increased, and new, bigger, bimatrix games are solved until an acceptable solution of the bimatrix game becomes sufficiently close to the same-type solutions at the preceding iterations. The closeness is expressed as the absolute difference between the trend-defining coefficients of the strategies from the neighboring solutions. These distances should be decreasing once they are smoothed with respective polynomials of degree 2. AMS Subject Classification: 91A05, 91A10, 65D99, 41A99.
{"title":"Finite Approximation of Continuous Noncooperative Two-person Games on a Product of Linear Strategy Functional Spaces","authors":"V. Romanuke","doi":"10.7862/rf.2020.9","DOIUrl":"https://doi.org/10.7862/rf.2020.9","url":null,"abstract":"A method of the finite approximation of continuous noncooperative two-person games is presented. The method is based on sampling the functional spaces, which serve as the sets of pure strategies of the players. The pure strategy is a linear function of time, in which the trenddefining coefficient is variable. The spaces of the players’ pure strategies are sampled uniformly so that the resulting finite game is a bimatrix game whose payoff matrices are square. The approximation procedure starts with not a great number of intervals. Then this number is gradually increased, and new, bigger, bimatrix games are solved until an acceptable solution of the bimatrix game becomes sufficiently close to the same-type solutions at the preceding iterations. The closeness is expressed as the absolute difference between the trend-defining coefficients of the strategies from the neighboring solutions. These distances should be decreasing once they are smoothed with respective polynomials of degree 2. AMS Subject Classification: 91A05, 91A10, 65D99, 41A99.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"30 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116714076","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}
{"title":"The Fourier method in three-dimensional dynamical problems of the hemitropic theory of elasticity","authors":"Y. Bezhuashvili, R. Rukhadze","doi":"10.7862/RF.2012.1","DOIUrl":"https://doi.org/10.7862/RF.2012.1","url":null,"abstract":"","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129592349","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}
In this paper we prove the interior approximate control- lability of the following Generalized Semilinear Benjamin-Bona-Mahony type equation (BBM) with homogeneous Dirichlet boundary conditions zt a zt b z = 1!u(t;x) +f(t;z;u(t;x)); t2 (0; ); x2 ; z(t;x) = 0; t 0; x2 @ ; where a 0 and b > 0 are constants, is a domain in IR N , ! is an open
本文证明了具有齐次Dirichlet边界条件zt a zt b z = 1!u(t;x) +f(t;z;u(t;x))的广义半线性Benjamin-Bona-Mahony型方程(BBM)的内部近似控制稳定性;T2 (0;);x2;Z (t;x) = 0;t 0;X2 @;其中a 0和b > 0是常数，是IR N中的定义域，!是开放的
{"title":"Controllability of the semilinear Benjamin-Bona-Mahony equation","authors":"H. Leiva, N. Merentes, J. Sánchez","doi":"10.7862/RF.2012.4","DOIUrl":"https://doi.org/10.7862/RF.2012.4","url":null,"abstract":"In this paper we prove the interior approximate control- lability of the following Generalized Semilinear Benjamin-Bona-Mahony type equation (BBM) with homogeneous Dirichlet boundary conditions zt a zt b z = 1!u(t;x) +f(t;z;u(t;x)); t2 (0; ); x2 ; z(t;x) = 0; t 0; x2 @ ; where a 0 and b > 0 are constants, is a domain in IR N , ! is an open","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126160143","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}
Throughout this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s value distribution theory on the complex plane and in the unit disc ∆ = {z : |z| < 1} (see [13] , [14] , [18] , [20]). We need to give some definitions and discussions. Firstly, let us give two definitions about the degree of small growth order of functions in ∆ as polynomials on the complex plane C. There are many types of definitions of small growth order of functions in ∆ (see [10] , [11]) .
{"title":"Properties of higher order differential polynomials generated by solutions of complex differential equations in the unit disc","authors":"Z. Latreuch, B. Belaïdi","doi":"10.7862/RF.2014.7","DOIUrl":"https://doi.org/10.7862/RF.2014.7","url":null,"abstract":"Throughout this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s value distribution theory on the complex plane and in the unit disc ∆ = {z : |z| < 1} (see [13] , [14] , [18] , [20]). We need to give some definitions and discussions. Firstly, let us give two definitions about the degree of small growth order of functions in ∆ as polynomials on the complex plane C. There are many types of definitions of small growth order of functions in ∆ (see [10] , [11]) .","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128442422","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}
The concept of 2-normed spaces was initially developed by Gähler [6] in the mid of 1960’s, while that of n-normed spaces one can see in Misiak [17]. Since then, many others have studied this concept and obtained various results, see Gunawan ([7], [8]) and Gunawan and Mashadi [9] and many others. Let n ∈ N and X be a linear space over the field K, where K is field of real or complex numbers of dimension d, where d ≥ n ≥ 2. A real valued function ||·, · · · , ·|| on X satisfying the following four conditions:
二范空间的概念最初是由Gähler[6]在20世纪60年代中期提出的，而n范空间的概念可以在Misiak[17]中看到。此后，许多人对这一概念进行了研究，并获得了各种结果，如Gunawan([7]，[8])和Gunawan and Mashadi[9]等。设n∈n, X为域K上的线性空间，其中K为维数为d的实数或复数域，且d≥n≥2。X上的实值函数||·，···，·||满足以下四个条件:
{"title":"Some seminormed difference sequence spaces defined by a Musielak-Orlicz function over n-normed spaces","authors":"K. Raj, S. Sharma","doi":"10.7862/RF.2015.10","DOIUrl":"https://doi.org/10.7862/RF.2015.10","url":null,"abstract":"The concept of 2-normed spaces was initially developed by Gähler [6] in the mid of 1960’s, while that of n-normed spaces one can see in Misiak [17]. Since then, many others have studied this concept and obtained various results, see Gunawan ([7], [8]) and Gunawan and Mashadi [9] and many others. Let n ∈ N and X be a linear space over the field K, where K is field of real or complex numbers of dimension d, where d ≥ n ≥ 2. A real valued function ||·, · · · , ·|| on X satisfying the following four conditions:","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"176 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114336962","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}
{"title":"De la Vallée Poussin Summability, the Combinatorial Sum ∑_(k=n)^(2n-1)▒〖(2k¦k) 〗 and the de la Vallée Poussin Means Expansion","authors":"Z. S. Ali","doi":"10.7862/RF.2017.1","DOIUrl":"https://doi.org/10.7862/RF.2017.1","url":null,"abstract":"","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114454100","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}
We dene two new general integral operators for certain analytic functions in the unit discU and give some sucient conditions for these integral operators on some subclasses of analytic functions.
{"title":"Starlikeness and convexity of certain integral operators defined by convolution","authors":"Jyoti Aggarwal, R. Mathur","doi":"10.7862/RF.2015.1","DOIUrl":"https://doi.org/10.7862/RF.2015.1","url":null,"abstract":"We dene two new general integral operators for certain analytic functions in the unit discU and give some sucient conditions for these integral operators on some subclasses of analytic functions.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130345342","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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