The primary goal of this paper is to present the generalization of begin{document}$ lambda $end{document}-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.
The primary goal of this paper is to present the generalization of begin{document}$ lambda $end{document}-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.
{"title":"The family of $ lambda $-Bernstein-Durrmeyer operators based on certain parameters","authors":"Ram Pratap","doi":"10.3934/mfc.2022038","DOIUrl":"https://doi.org/10.3934/mfc.2022038","url":null,"abstract":"<p style='text-indent:20px;'>The primary goal of this paper is to present the generalization of <inline-formula><tex-math id=\"M2\">begin{document}$ lambda $end{document}</tex-math></inline-formula>-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [<xref ref-type=\"bibr\" rid=\"b24\">24</xref>]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74024602","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 current paper, we are using the concept of extension of the beta function to define an extended $ k $-generalized Mittag-Leffler function (GMLf) $ E_{k, l, m}^{rho, sigma;c}(x;p) $. There are four sections included in this paper containing some properties of the above-described function, like derivatives, integral representation, and integral transform. The establishment of some recurrence relations has also been done. We also derive the extended $ k $-GMLf from the extended $ k $-Riemann-Liouville (R-L) fractional derivative of generalized MLf. Numerous former results studied by many researchers can also be derived as special cases of our results.
在本文中，我们使用beta函数扩展的概念来定义一个扩展$ k $ -广义Mittag-Leffler函数(GMLf) $ E_{k, l, m}^{rho, sigma;c}(x;p) $。本文分四节介绍了上述函数的一些性质，如导数、积分表示和积分变换。并建立了一些递推关系。我们还从广义MLf的扩展的$ k $ -Riemann-Liouville (R-L)分数阶导数中导出了扩展的$ k $ -GMLf。以前许多研究者研究过的许多结果，也可以作为我们研究结果的特殊情况推导出来。
{"title":"On extended $ k $-generalized Mittag-Leffler function and its properties","authors":"Shilpi Jain, B.B. Jaimini, Meenu Buri, Praveen Agarwal","doi":"10.3934/mfc.2023041","DOIUrl":"https://doi.org/10.3934/mfc.2023041","url":null,"abstract":"In this current paper, we are using the concept of extension of the beta function to define an extended $ k $-generalized Mittag-Leffler function (GMLf) $ E_{k, l, m}^{rho, sigma;c}(x;p) $. There are four sections included in this paper containing some properties of the above-described function, like derivatives, integral representation, and integral transform. The establishment of some recurrence relations has also been done. We also derive the extended $ k $-GMLf from the extended $ k $-Riemann-Liouville (R-L) fractional derivative of generalized MLf. Numerous former results studied by many researchers can also be derived as special cases of our results.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the notion of multivalued rational type begin{document}$ F- $end{document} contraction mappings and prove fixed point theorems for this type mappings. Also we give an illustrative example.
In this paper, we consider the notion of multivalued rational type begin{document}$ F- $end{document} contraction mappings and prove fixed point theorems for this type mappings. Also we give an illustrative example.
{"title":"Multivalued rational type F-contraction on orthogonal metric space","authors":"Ö. Acar, A. S. Özkapu","doi":"10.3934/mfc.2022026","DOIUrl":"https://doi.org/10.3934/mfc.2022026","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we consider the notion of multivalued rational type <inline-formula><tex-math id=\"M1\">begin{document}$ F- $end{document}</tex-math></inline-formula> contraction mappings and prove fixed point theorems for this type mappings. Also we give an illustrative example.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84667887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund begin{document}$ (D^{h}_{g}N^{a,b}) $end{document} transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.
In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund begin{document}$ (D^{h}_{g}N^{a,b}) $end{document} transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.
{"title":"Degree of convergence of a function in generalized Zygmund space","authors":"H. K. Nigam, M. Mursaleen, M. Sah","doi":"10.3934/mfc.2022029","DOIUrl":"https://doi.org/10.3934/mfc.2022029","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund <inline-formula><tex-math id=\"M1\">begin{document}$ (D^{h}_{g}N^{a,b}) $end{document}</tex-math></inline-formula> transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77787626","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":"Fuzzy stability of mixed type functional equations in Modular spaces","authors":"Jagjeet Jakhar, Jyotsana Jakhar, R. Chugh","doi":"10.3934/mfc.2023019","DOIUrl":"https://doi.org/10.3934/mfc.2023019","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220642","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":"Parameters identification and trajectory optimization of free-floating space robots","authors":"Deshan Meng, Yanan Li, Ruiqi Wang, Xudong Zheng","doi":"10.3934/mfc.2023027","DOIUrl":"https://doi.org/10.3934/mfc.2023027","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221037","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":"A new hybrid CG method as convex combination","authors":"Amina Hallal, M. Belloufi, B. Sellami","doi":"10.3934/mfc.2023028","DOIUrl":"https://doi.org/10.3934/mfc.2023028","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221056","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 note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.
{"title":"Approximation by pseudo-linear discrete operators","authors":"Ismail Aslan, Türkan Yeliz Gökçer","doi":"10.3934/mfc.2021037","DOIUrl":"https://doi.org/10.3934/mfc.2021037","url":null,"abstract":"In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77651541","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 article, we define a new operator by Appell polynomials. Primarily, some equations are obtained by using the properties of Korovkin theorem. Later, the convergence of the operator sequence that we have defined has been proved and some approximation results have been given by using the properties of approximation theory.
{"title":"A generalization of szász operators with the help of new kind Appell polynomials","authors":"Gürhan İÇÖZ, Zehra Tat","doi":"10.3934/mfc.2023038","DOIUrl":"https://doi.org/10.3934/mfc.2023038","url":null,"abstract":"In this article, we define a new operator by Appell polynomials. Primarily, some equations are obtained by using the properties of Korovkin theorem. Later, the convergence of the operator sequence that we have defined has been proved and some approximation results have been given by using the properties of approximation theory.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135557381","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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