The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained resul...The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.展开更多
In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered B...In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.展开更多
In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative...In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.展开更多
In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].
In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term ...In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term consequences that businesses encounter. This study integrates findings from various research, including quantitative reports, drawing upon real-world incidents faced by both small and large enterprises. This investigation emphasizes the profound intangible costs, such as trade name devaluation and potential damage to brand reputation, which can persist long after the breach. By collating insights from industry experts and a myriad of research, the study provides a comprehensive perspective on the profound, multi-dimensional impacts of cybersecurity incidents. The overarching aim is to underscore the often-underestimated scope and depth of these breaches, emphasizing the entire timeline post-incident and the urgent need for fortified preventative and reactive measures in the digital domain.展开更多
Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to...Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.展开更多
Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞)...Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞) by using this theorem.展开更多
文摘The minimal-maximal fixed points theorems of increasing operators are proved in ordered space and some well-known results of increasing operators and monotone operators are improved and generalized. The obtained results are then applied to singular nonlinear boundary problem in ordinary differential equation without any assumption of continuity, compactness, convexity and concavity.
基金Funded by the Natural Science Foundation of China (No. 10171070)
文摘In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.
文摘In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.
文摘In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].
文摘In this in-depth exploration, I delve into the complex implications and costs of cybersecurity breaches. Venturing beyond just the immediate repercussions, the research unearths both the overt and concealed long-term consequences that businesses encounter. This study integrates findings from various research, including quantitative reports, drawing upon real-world incidents faced by both small and large enterprises. This investigation emphasizes the profound intangible costs, such as trade name devaluation and potential damage to brand reputation, which can persist long after the breach. By collating insights from industry experts and a myriad of research, the study provides a comprehensive perspective on the profound, multi-dimensional impacts of cybersecurity incidents. The overarching aim is to underscore the often-underestimated scope and depth of these breaches, emphasizing the entire timeline post-incident and the urgent need for fortified preventative and reactive measures in the digital domain.
文摘Some new results about the NBU(2) class of life distributions were obtained. Fir stly, it was proved that the decrease with time of the increasing concave orderi ng of the excess lifetime in a renewal process leads to the NBU(2) property of t he interarrival times. Secondly, the NBU(2) class of life distributions is prove d to be closed under the formation of series systems. Finally, it was also shown that the NBU(2) class is closed under convolution operation.
文摘Presents the fixed point theorem for a class of β constrictive increasing operators without continuity and discusses the existence of solution of the integral equation with the discontinuous term in L 1(0,∞) by using this theorem.
