The present paper deals with complex form of a generalization of perturbed Bernstein-type operators. Quantitative upper estimates for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation by these operators attached to functions analytic in a disk centered at the origin with radius greater than 1 are obtained in this study.
{"title":"On complex modified Bernstein-Stancu operators","authors":"N. Çetin","doi":"10.3934/mfc.2021043","DOIUrl":"https://doi.org/10.3934/mfc.2021043","url":null,"abstract":"The present paper deals with complex form of a generalization of perturbed Bernstein-type operators. Quantitative upper estimates for simultaneous approximation, a qualitative Voronovskaja type result and the exact order of approximation by these operators attached to functions analytic in a disk centered at the origin with radius greater than 1 are obtained in this study.","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":"87530067","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":"Dynamically consistent nonstandard numerical schemes for solving some computer virus and malware propagation models","authors":"M. T. Hoang, Thi Kim Quy Ngo, D. H. Tran","doi":"10.3934/mfc.2022042","DOIUrl":"https://doi.org/10.3934/mfc.2022042","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":"85446186","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":"Integral Baskakov type operator with quadratic order of approximation","authors":"A. R. Gairola, Amrita Singh","doi":"10.3934/mfc.2022051","DOIUrl":"https://doi.org/10.3934/mfc.2022051","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":"83410687","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 function begin{document}$ varphi_L $end{document} defined by begin{document}$ varphi_L(z) = sqrt{1+z} $end{document} maps the unit disk begin{document}$ mathbb{D} $end{document} onto begin{document}$ Omega = {winmathbb{C}: |w^2-1|<1} $end{document}, the region in the right half-plane bounded by the lemniscate of Bernoulli begin{document}$ |w^2-1| = 1 $end{document}. This paper deals with starlike functions defined on begin{document}$ mathbb{D} $end{document} with begin{document}$ zf'(z)/f(z)in Omega $end{document} or equivalently begin{document}$ zf'(z)/f(z) $end{document} is subordinated to begin{document}$ varphi_L(z) $end{document} and these functions are related to the analytic function begin{document}$ p:mathbb{D}to mathbb{C} $end{document} with begin{document}$ p(z)in Omega $end{document} for all begin{document}$ zin mathbb{D} $end{document} by begin{document}$ p(z) = zf'(z)/f(z) $end{document}. Using the admissibility criteria of the first and second order differential subordination, we investigate several subordination results for functions begin{document}$ p $end{document} to satisfy begin{document}$ p(z)in Omega $end{document}. As applications, we give several sufficient conditions for functions begin{document}$ f $end{document} to satisfy begin{document}$ zf'(z)/f(z)in Omega $end{document}.
{"title":"Analytic function that map the unit disk into the inside of the lemniscate of Bernoulli","authors":"Shalu Yadav, Vaithiyanathan Ravichandran","doi":"10.3934/mfc.2022036","DOIUrl":"https://doi.org/10.3934/mfc.2022036","url":null,"abstract":"<p style='text-indent:20px;'>The function <inline-formula><tex-math id=\"M5\">begin{document}$ varphi_L $end{document}</tex-math></inline-formula> defined by <inline-formula><tex-math id=\"M6\">begin{document}$ varphi_L(z) = sqrt{1+z} $end{document}</tex-math></inline-formula> maps the unit disk <inline-formula><tex-math id=\"M7\">begin{document}$ mathbb{D} $end{document}</tex-math></inline-formula> onto <inline-formula><tex-math id=\"M8\">begin{document}$ Omega = {winmathbb{C}: |w^2-1|<1} $end{document}</tex-math></inline-formula>, the region in the right half-plane bounded by the lemniscate of Bernoulli <inline-formula><tex-math id=\"M9\">begin{document}$ |w^2-1| = 1 $end{document}</tex-math></inline-formula>. This paper deals with starlike functions defined on <inline-formula><tex-math id=\"M10\">begin{document}$ mathbb{D} $end{document}</tex-math></inline-formula> with <inline-formula><tex-math id=\"M11\">begin{document}$ zf'(z)/f(z)in Omega $end{document}</tex-math></inline-formula> or equivalently <inline-formula><tex-math id=\"M12\">begin{document}$ zf'(z)/f(z) $end{document}</tex-math></inline-formula> is subordinated to <inline-formula><tex-math id=\"M13\">begin{document}$ varphi_L(z) $end{document}</tex-math></inline-formula> and these functions are related to the analytic function <inline-formula><tex-math id=\"M14\">begin{document}$ p:mathbb{D}to mathbb{C} $end{document}</tex-math></inline-formula> with <inline-formula><tex-math id=\"M15\">begin{document}$ p(z)in Omega $end{document}</tex-math></inline-formula> for all <inline-formula><tex-math id=\"M16\">begin{document}$ zin mathbb{D} $end{document}</tex-math></inline-formula> by <inline-formula><tex-math id=\"M17\">begin{document}$ p(z) = zf'(z)/f(z) $end{document}</tex-math></inline-formula>. Using the admissibility criteria of the first and second order differential subordination, we investigate several subordination results for functions <inline-formula><tex-math id=\"M18\">begin{document}$ p $end{document}</tex-math></inline-formula> to satisfy <inline-formula><tex-math id=\"M19\">begin{document}$ p(z)in Omega $end{document}</tex-math></inline-formula>. As applications, we give several sufficient conditions for functions <inline-formula><tex-math id=\"M20\">begin{document}$ f $end{document}</tex-math></inline-formula> to satisfy <inline-formula><tex-math id=\"M21\">begin{document}$ zf'(z)/f(z)in Omega $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86136170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this paper, we consider the two-layer begin{document}$ (a, b) $end{document} dividend strategy when the risk process is modeled by a spectrally negative Lévy process, such a strategy has an increasing dividend rate when the surplus exceeds level begin{document}$ a>0 $end{document}, and all of the excess over begin{document}$ b>a $end{document} as lump sum dividend payments. Using fluctuation identities and scale functions, we obtain explicit formulas for the expected net present value of dividends until ruin and the Laplace transform of the time to ruin. Finally, numerical illustrations are present to show the impacts of parameters on the expected net present value.
The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this paper, we consider the two-layer begin{document}$ (a, b) $end{document} dividend strategy when the risk process is modeled by a spectrally negative Lévy process, such a strategy has an increasing dividend rate when the surplus exceeds level begin{document}$ a>0 $end{document}, and all of the excess over begin{document}$ b>a $end{document} as lump sum dividend payments. Using fluctuation identities and scale functions, we obtain explicit formulas for the expected net present value of dividends until ruin and the Laplace transform of the time to ruin. Finally, numerical illustrations are present to show the impacts of parameters on the expected net present value.
{"title":"A Lévy risk model with ratcheting and barrier dividend strategies","authors":"Hui Gao, C. Yin","doi":"10.3934/mfc.2022025","DOIUrl":"https://doi.org/10.3934/mfc.2022025","url":null,"abstract":"<p style='text-indent:20px;'>The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this paper, we consider the two-layer <inline-formula><tex-math id=\"M1\">begin{document}$ (a, b) $end{document}</tex-math></inline-formula> dividend strategy when the risk process is modeled by a spectrally negative Lévy process, such a strategy has an increasing dividend rate when the surplus exceeds level <inline-formula><tex-math id=\"M2\">begin{document}$ a>0 $end{document}</tex-math></inline-formula>, and all of the excess over <inline-formula><tex-math id=\"M3\">begin{document}$ b>a $end{document}</tex-math></inline-formula> as lump sum dividend payments. Using fluctuation identities and scale functions, we obtain explicit formulas for the expected net present value of dividends until ruin and the Laplace transform of the time to ruin. Finally, numerical illustrations are present to show the impacts of parameters on the expected net present value.</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":"88418847","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":"Approximation properties of exponential type operators connected to $ p(x) = 2x^{3/2} $","authors":"Carmen Muraru Popescu, V. Radu","doi":"10.3934/mfc.2022055","DOIUrl":"https://doi.org/10.3934/mfc.2022055","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":"89149142","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}
Sirajo Yahaya, Mohammed Shehu Shagari, Tijjani Abba Ali
In this manuscript, a new concept of multivalued contraction is defined from a combination of Jaggi-type contractions, interpolative-type contraction and Pata-type inequality in the framework of metric space, and we analyze the existence of fixed points for such contractions equipped with some suitable hypotheses. One of the motivations forming the background of this paper is the fact that fixed point of a single-valued mapping satisfying the interpolative contractive condition is not necessarily unique, and thereby making the notions more appropriate for fixed point theorems of multi-valued mappings. A few salient consequences, including the single-valued cases are highlighted and discussed to indicate the significance of our proposed ideas. Also we give a comparative example.
{"title":"Multivalued hybrid contraction that involves Jaggi and Pata-type inequalities","authors":"Sirajo Yahaya, Mohammed Shehu Shagari, Tijjani Abba Ali","doi":"10.3934/mfc.2023045","DOIUrl":"https://doi.org/10.3934/mfc.2023045","url":null,"abstract":"In this manuscript, a new concept of multivalued contraction is defined from a combination of Jaggi-type contractions, interpolative-type contraction and Pata-type inequality in the framework of metric space, and we analyze the existence of fixed points for such contractions equipped with some suitable hypotheses. One of the motivations forming the background of this paper is the fact that fixed point of a single-valued mapping satisfying the interpolative contractive condition is not necessarily unique, and thereby making the notions more appropriate for fixed point theorems of multi-valued mappings. A few salient consequences, including the single-valued cases are highlighted and discussed to indicate the significance of our proposed ideas. Also we give a comparative example.","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":"135709284","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}
P. Garrancho, Francisco-Javier Martínez-Sánchez, D. Cárdenas-Morales
{"title":"Approximation rate and saturation under generalized convergence","authors":"P. Garrancho, Francisco-Javier Martínez-Sánchez, D. Cárdenas-Morales","doi":"10.3934/mfc.2023002","DOIUrl":"https://doi.org/10.3934/mfc.2023002","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":"70220005","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":"Solution of Abel's integral equation by modified Taylor wavelet with error analysis","authors":"Shyam Lal, Satish Kumar","doi":"10.3934/mfc.2023009","DOIUrl":"https://doi.org/10.3934/mfc.2023009","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":"70220502","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 work we will discuss about an approximation method for initial value problems associated to fractional order differential equations. For this method we will use Bernstein spline approximation in combination with the Banach's Fixed Point Theorem. In order to illustrate our results, some numerical examples will be presented at the end of this article.
{"title":"Iterative Bernstein splines technique applied to fractional order differential equations","authors":"Z. Satmari","doi":"10.3934/mfc.2021039","DOIUrl":"https://doi.org/10.3934/mfc.2021039","url":null,"abstract":"In this work we will discuss about an approximation method for initial value problems associated to fractional order differential equations. For this method we will use Bernstein spline approximation in combination with the Banach's Fixed Point Theorem. In order to illustrate our results, some numerical examples will be presented at the end of this article.","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":"80915974","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：