Pub Date : 2020-07-01DOI: 10.18311/jims/2020/25452
D. C. Pramanik, Jayanta Roy
In this paper, we study the uniqueness for meromorphic functions when they share a set of roots of unity.
本文研究了亚纯函数共用一组统一根时的唯一性问题。
{"title":"Uniqueness of Meromorphic Functions Sharing a Set of Roots of Unity","authors":"D. C. Pramanik, Jayanta Roy","doi":"10.18311/jims/2020/25452","DOIUrl":"https://doi.org/10.18311/jims/2020/25452","url":null,"abstract":"In this paper, we study the uniqueness for meromorphic functions when they share a set of roots of unity.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44223567","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 : 2020-07-01DOI: 10.18311/jims/2020/25454
R. Srivastava, Y. Singh
The object of this paper is to demonstrate the existence, explicit characterization and estimation of the polynomial interpolation, related to the weighted (0;0,2) interpolation which satisfies the boundary conditions together with the interpolation conditions at the interval [−1, 1].
{"title":"A (0;0,2) Interpolation Method to Approximate Functions via Ultraspherical Polynomials","authors":"R. Srivastava, Y. Singh","doi":"10.18311/jims/2020/25454","DOIUrl":"https://doi.org/10.18311/jims/2020/25454","url":null,"abstract":"The object of this paper is to demonstrate the existence, explicit characterization and estimation of the polynomial interpolation, related to the weighted (0;0,2) interpolation which satisfies the boundary conditions together with the interpolation conditions at the interval [−1, 1].","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49282079","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 : 2020-07-01DOI: 10.18311/jims/2020/23906
Saroj Rani
In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8ps over the chain ring Fpm + uFpm in terms of their generator polynomials, where u2 = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8ps over Fpm + uFpm. Also, we determine μ and -constacyclic codes of length 8ps over Fpm + uFpm.
{"title":"On Cyclic and Negacyclic Codes of Length 8ps Over Fpm + uFpm","authors":"Saroj Rani","doi":"10.18311/jims/2020/23906","DOIUrl":"https://doi.org/10.18311/jims/2020/23906","url":null,"abstract":"In this paper, we establish the algebraic structure of all cyclic and negacyclic codes of length 8<em>p</em><sup>s</sup> over the chain ring Fp<sup>m</sup> + uFp<sup>m</sup> in terms of their generator polynomials, where u<sup>2</sup> = 0 and s is a positive integer and p is an odd prime. We also find out the number of codewords in each of these cyclic codes. Besides this, we determine duals of cyclic codes and list self-dual cyclic and negacyclic codes of length 8<em>p</em><sup>s</sup> over Fp<sup>m</sup> + uFp<sup>m</sup>. Also, we determine μ and -constacyclic codes of length 8<em>p</em><sup>s</sup> over Fp<sup>m</sup> + uFp<sup>m</sup>.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47333717","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 : 2020-07-01DOI: 10.18311/JIMS/2020/24607
M. Andrić, G. Farid, J. Pečarić, Usama Siddique
In this paper the reverse fractional Minkowski integral inequality using extended Mittag-Leffler function with the corresponding fractional integral operator is proved, as well as several related Minkowskitype inequalities.
{"title":"Generalized Minkowski-type Fractional Inequalities Involving Extended Mittag-leffler Function","authors":"M. Andrić, G. Farid, J. Pečarić, Usama Siddique","doi":"10.18311/JIMS/2020/24607","DOIUrl":"https://doi.org/10.18311/JIMS/2020/24607","url":null,"abstract":"In this paper the reverse fractional Minkowski integral inequality using extended Mittag-Leffler function with the corresponding fractional integral operator is proved, as well as several related Minkowskitype inequalities.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46463998","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 : 2020-05-15DOI: 10.18311/JIMS/2020/21297
G. S. Rathore, Tripti Mittal
In the present paper, we study perturbation of weighted g −Banach frames in Banach spaces and obtain perturbation results for weighted g −Banach frames. Also, sufficient conditions for the perturbation of weighted g −Banach frames by positively confined sequence of scalars and uniformly scaled version of a given weighted g −Banach Bessel sequence have been given. Finally, we give a condition under which the sum of finite number of sequences of operators is a weighted g −Banach frame by comparing each of the sequences with another system of weighted g −Banach frames in Banach spaces.
{"title":"On Perturbation of Weighted G−Banach Frames in Banach Spaces","authors":"G. S. Rathore, Tripti Mittal","doi":"10.18311/JIMS/2020/21297","DOIUrl":"https://doi.org/10.18311/JIMS/2020/21297","url":null,"abstract":"In the present paper, we study perturbation of weighted g −Banach frames in Banach spaces and obtain perturbation results for weighted g −Banach frames. Also, sufficient conditions for the perturbation of weighted g −Banach frames by positively confined sequence of scalars and uniformly scaled version of a given weighted g −Banach Bessel sequence have been given. Finally, we give a condition under which the sum of finite number of sequences of operators is a weighted g −Banach frame by comparing each of the sequences with another system of weighted g −Banach frames in Banach spaces.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44713809","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 : 2020-05-15DOI: 10.18311/jims/2020/22506
A. Das, S. K. Paikray, T. Pradhan, H. Dutta
Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class W(Z r (ω) ) by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.
{"title":"Approximation of Signals in the Weighted Zygmund Class Via Euler-hausdorff Product Summability Mean of Fourier Series","authors":"A. Das, S. K. Paikray, T. Pradhan, H. Dutta","doi":"10.18311/jims/2020/22506","DOIUrl":"https://doi.org/10.18311/jims/2020/22506","url":null,"abstract":"Approximation of functions of Lipschitz and zygmund classes have been considered by various researchers under different summability means. In the proposed paper, we have studied an estimation of the order of convergence of Fourier series in the weighted Zygmund class W(Z r (ω) ) by using Euler-Hausdorff product summability mean and accordingly established some (presumably new) results. Moreover, the results obtained here are the generalization of several known results.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42338665","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 : 2020-05-15DOI: 10.18311/jims/2020/23248
N. Gupta, J. P. Jaiswal
The motive of this article is to analyze the semilocal convergence of a well existing iterative method in the Banach spaces to get the solution of nonlinear equations. The condition, we assume that the nonlinear operator fulfills the Hölder continuity condition which is softer than the Lipschitz continuity and works on the problems in which either second order Frèchet derivative of the nonlinear operator is challenging to calculate or does not hold the Lipschitz condition. In the convergence theorem, the existence of the solution x* and its uniqueness along with prior error bound are established. Also, the R-order of convergence for this method is proved to be at least 4+3q. Two numerical examples are discussed to justify the included theoretical development followed by an error bound expression.
{"title":"Semilocal Convergence of a Seventh-Order Method in Banach Spaces Under Hölder Continuity Condition","authors":"N. Gupta, J. P. Jaiswal","doi":"10.18311/jims/2020/23248","DOIUrl":"https://doi.org/10.18311/jims/2020/23248","url":null,"abstract":"The motive of this article is to analyze the semilocal convergence of a well existing iterative method in the Banach spaces to get the solution of nonlinear equations. The condition, we assume that the nonlinear operator fulfills the Hölder continuity condition which is softer than the Lipschitz continuity and works on the problems in which either second order Frèchet derivative of the nonlinear operator is challenging to calculate or does not hold the Lipschitz condition. In the convergence theorem, the existence of the solution x* and its uniqueness along with prior error bound are established. Also, the R-order of convergence for this method is proved to be at least 4+3q. Two numerical examples are discussed to justify the included theoretical development followed by an error bound expression.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47102538","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 : 2020-05-15DOI: 10.18311/jims/2020/24428
S. Datta, Banani Dutta, Nityagopal Biswas
In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.
{"title":"On Different Relative Growth Factors of Entire Functions","authors":"S. Datta, Banani Dutta, Nityagopal Biswas","doi":"10.18311/jims/2020/24428","DOIUrl":"https://doi.org/10.18311/jims/2020/24428","url":null,"abstract":"In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45972380","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 : 2020-05-15DOI: 10.18311/jims/2020/22695
Aparna Chaturvedi, Prakriti Rai
In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials. We have shown that there is an intimate connection between these polynomials and derived some implicit summation formulae by applying the generating functions.
{"title":"Generalized Hermite- based Apostol- Bernoulli, Euler, Genocchi polynomials and their relations","authors":"Aparna Chaturvedi, Prakriti Rai","doi":"10.18311/jims/2020/22695","DOIUrl":"https://doi.org/10.18311/jims/2020/22695","url":null,"abstract":"In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials. We have shown that there is an intimate connection between these polynomials and derived some implicit summation formulae by applying the generating functions.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42031693","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":"Shift Balancing Numbers","authors":"S. G. Rayaguru, G. Panda, R. K. Davala","doi":"10.18311/jims/2020/24872","DOIUrl":"https://doi.org/10.18311/jims/2020/24872","url":null,"abstract":"For each positive integer k , the Diophantine equation (k+1)+(k+2)+···+(n−1) = (n+1)+(n+2)+···+(n+r) is studied.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44316127","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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