In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the...In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.展开更多
In this paper,we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function,which generalizes the Riemann-Liouville fractional integral and t...In this paper,we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function,which generalizes the Riemann-Liouville fractional integral and the Hadaniard fractional integral.We establish an existence result to such kind of equations using a generalized version of Darbo＇s theorem associated to a certain measure of nonconipactness.Some examples are presented.展开更多
The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators...The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F（x） = αx （α≥1） for such class of operators. As consequences, the main results general- ize and improve the relevant results, which are obtained by O＇Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive （μ-nonexpansive） and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.展开更多
BACKGROUND Left ventricular noncompaction(LVNC)is a genetic cardiomyopathy.It is characterized by intensely developed trabeculae in the ventricles with deep intertrabecular lacunae.LVNC manifests as arrhythmias and he...BACKGROUND Left ventricular noncompaction(LVNC)is a genetic cardiomyopathy.It is characterized by intensely developed trabeculae in the ventricles with deep intertrabecular lacunae.LVNC manifests as arrhythmias and heart failure with a predisposition for thrombus formation.AIM To study predictors of arrhythmic,thromboembolic events and adverse outcomes(death/transplantation)in adult patients with LVNC.METHODS Adult patients with LVNC were included(n=125;mean follow-up:14 months).Electrocardiography,echocardiography,and 24-hour electrocardiography monitoring were performed.Other procedures were conducted for some patients including:Coronary angiography;cardiac magnetic resonance imaging;cardiac computed tomography;genetic testing;myocardial pathological examination;and anti-cardiac antibody level estimation.Primary endpoints were death,heart transplantation,combined endpoint(death+transplantation),and sudden cardiac death.Secondary endpoints were intracardiac thrombosis,embolic events,myocardial infarction,sustained ventricular tachycardia(VT),and implantable cardioverter-defibrillator intervention.RESULTS LVNC manifestations included non-sustained VT,thrombosis/embolism,sustained VT, and sudden cardiac death. Non-sustained VT was associated with the New York Heart Association(NYHA) chronic heart failure (CHF) class, poor R-wave progression, superimposed myocarditis, and highermortality. Thrombosis/embolism was associated with NYHA CHF class ≥ 3, right ventricular end-diastolicdiameter ≥ 3 cm, right atrium volume ≥ 67 mL, left ventricle end-diastolic diameter ≥ 6.3 cm, and velocity timeintegral ≤ 11.2 cm. Sustained VT was associated with premature ventricular contractions (PVCs), low QRS voltage,and atrioventricular block. PVCs > 500/day were predictive of defibrillator intervention. Fatal outcomes wereassociated with E wave/A wave ratio > 1.9, left ventricle ejection fraction < 35%, NYHA CHF class ≥ 3, VT, andmyocarditis.CONCLUSIONFrequent PVCs, non-sustained VT, low QRS voltage, and signs of systolic dysfunction on echocardiogram arepredictors of life-threatening events in patients with LVNC.展开更多
This paper is devoted to the existence results for a class of neutral abstract fractional differential equations involving the composite relaxation process.Based on the Laplace transform,the semigroup theory and the W...This paper is devoted to the existence results for a class of neutral abstract fractional differential equations involving the composite relaxation process.Based on the Laplace transform,the semigroup theory and the Wright functions,we first introduce a definition of mild solutions to the considered problem.By means of the noncompactness of measure and the fixed point technique,we establish existence criteria of solutions.Finally,an example is presented to illustrate our main result.展开更多
文摘In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.
基金support by the Ministerio de Economica y Competitividad of Spain under grant MTM2013-43014-PXUNTA under grants R2014/002 and GRC2015/004+1 种基金co-financed by the European Community fund FEDERextends his appreciation to Distinguished Scientist Fellowship Program(DSFP)at King Saud University(Saudi Arabia)
文摘In this paper,we study the existence of solutions to an implicit functional equation involving a fractional integral with respect to a certain function,which generalizes the Riemann-Liouville fractional integral and the Hadaniard fractional integral.We establish an existence result to such kind of equations using a generalized version of Darbo＇s theorem associated to a certain measure of nonconipactness.Some examples are presented.
基金Supported in part by the Foundation of Hanshan Normal University, China
文摘The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F（x） = αx （α≥1） for such class of operators. As consequences, the main results general- ize and improve the relevant results, which are obtained by O＇Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive （μ-nonexpansive） and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.
文摘BACKGROUND Left ventricular noncompaction(LVNC)is a genetic cardiomyopathy.It is characterized by intensely developed trabeculae in the ventricles with deep intertrabecular lacunae.LVNC manifests as arrhythmias and heart failure with a predisposition for thrombus formation.AIM To study predictors of arrhythmic,thromboembolic events and adverse outcomes(death/transplantation)in adult patients with LVNC.METHODS Adult patients with LVNC were included(n=125;mean follow-up:14 months).Electrocardiography,echocardiography,and 24-hour electrocardiography monitoring were performed.Other procedures were conducted for some patients including:Coronary angiography;cardiac magnetic resonance imaging;cardiac computed tomography;genetic testing;myocardial pathological examination;and anti-cardiac antibody level estimation.Primary endpoints were death,heart transplantation,combined endpoint(death+transplantation),and sudden cardiac death.Secondary endpoints were intracardiac thrombosis,embolic events,myocardial infarction,sustained ventricular tachycardia(VT),and implantable cardioverter-defibrillator intervention.RESULTS LVNC manifestations included non-sustained VT,thrombosis/embolism,sustained VT, and sudden cardiac death. Non-sustained VT was associated with the New York Heart Association(NYHA) chronic heart failure (CHF) class, poor R-wave progression, superimposed myocarditis, and highermortality. Thrombosis/embolism was associated with NYHA CHF class ≥ 3, right ventricular end-diastolicdiameter ≥ 3 cm, right atrium volume ≥ 67 mL, left ventricle end-diastolic diameter ≥ 6.3 cm, and velocity timeintegral ≤ 11.2 cm. Sustained VT was associated with premature ventricular contractions (PVCs), low QRS voltage,and atrioventricular block. PVCs > 500/day were predictive of defibrillator intervention. Fatal outcomes wereassociated with E wave/A wave ratio > 1.9, left ventricle ejection fraction < 35%, NYHA CHF class ≥ 3, VT, andmyocarditis.CONCLUSIONFrequent PVCs, non-sustained VT, low QRS voltage, and signs of systolic dysfunction on echocardiogram arepredictors of life-threatening events in patients with LVNC.
基金Supported by the Guangxi Science and Technology base and Talent Project(AD23026249,AD22080047).
文摘This paper is devoted to the existence results for a class of neutral abstract fractional differential equations involving the composite relaxation process.Based on the Laplace transform,the semigroup theory and the Wright functions,we first introduce a definition of mild solutions to the considered problem.By means of the noncompactness of measure and the fixed point technique,we establish existence criteria of solutions.Finally,an example is presented to illustrate our main result.
