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 $-Riemann-Liouville (R-L) fractional derivative of generalized MLf. Numerous former results studied by many researchers can also be derived as special cases of our results.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we consider a general class of operators enriched with some properties in order to act on begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document}. We establish uniform convergence of the operators for every function in begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document} on begin{document}$ mathbb{R} _{0}^{+} $end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.
In the present paper, we consider a general class of operators enriched with some properties in order to act on begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document}. We establish uniform convergence of the operators for every function in begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document} on begin{document}$ mathbb{R} _{0}^{+} $end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.
{"title":"On a special class of modified integral operators preserving some exponential functions","authors":"G. Uysal","doi":"10.3934/mfc.2021044","DOIUrl":"https://doi.org/10.3934/mfc.2021044","url":null,"abstract":"<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id=\"M1\">begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id=\"M2\">begin{document}$ C^{ast }( mathbb{R} _{0}^{+}) $end{document}</tex-math></inline-formula> on <inline-formula><tex-math id=\"M3\">begin{document}$ mathbb{R} _{0}^{+} $end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":"78-93"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83126343","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":"84 1","pages":"1-13"},"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 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}) $end{document}</tex-math></inline-formula> transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"8 1","pages":"484-499"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77787626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the notion of multivalued rational type begin{document}$ 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":"7 1","pages":"303-312"},"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}
{"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":"1 1","pages":""},"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":"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":"1 1","pages":""},"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 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":"66 1","pages":"0"},"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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