In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. ...In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.展开更多
In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Bana...In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions.展开更多
In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with...In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2 u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecrcasing with respect to s for all x ∈Ω and some others. In this paper. by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.展开更多
This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of...This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.展开更多
Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs...Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.展开更多
We consider a discrete-time risk model,in which insurance risks and financial risks jointly follow a multivariate Farlie-Gumbel-Morgenstern distribution,and the insurance risks are regularly varying tailed.Explicit as...We consider a discrete-time risk model,in which insurance risks and financial risks jointly follow a multivariate Farlie-Gumbel-Morgenstern distribution,and the insurance risks are regularly varying tailed.Explicit asymptotic formulae are obtained for finite-time and infinite-time ruin probabilities.Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae.展开更多
基金supported by the Province Natural Science Foundation of China(2014J01008)
文摘In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2014J01008)
文摘In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions.
基金the National Natural Science Foundation of China (No.19871030)the Guangdong Provincial Natural Science Foundation of China (No.980587).
文摘In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2 u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecrcasing with respect to s for all x ∈Ω and some others. In this paper. by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.
基金supported by the National Science Foundation of China under Grant No.11071182the fund of Nanjing University of Information Science and Technology under Grant No.Y627
文摘This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.
基金Supported by the National Natural Science Foundation of China(11301481,11201422,11371321)Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)Foundation for Young Talents of ZJGSU(1020XJ1314019)
文摘Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.
基金supported by National Natural Science Foundation of China(Grant Nos.10801124 and 11171321)the Fundamental Research Funds for the Central Universities(GrantNo.WK 2040170006)
文摘We consider a discrete-time risk model,in which insurance risks and financial risks jointly follow a multivariate Farlie-Gumbel-Morgenstern distribution,and the insurance risks are regularly varying tailed.Explicit asymptotic formulae are obtained for finite-time and infinite-time ruin probabilities.Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae.
