The goal of the present paper is to establish some new approach on the basic integral inequality of Gronwall-Bellman type and its generalizations involving function of one independent variable which provides explicit ...The goal of the present paper is to establish some new approach on the basic integral inequality of Gronwall-Bellman type and its generalizations involving function of one independent variable which provides explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential and integral equations.展开更多
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.
In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which gi...In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.展开更多
In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional ...In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.展开更多
In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function...In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function.展开更多
A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-a...A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).展开更多
The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve ...The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.展开更多
By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the res...By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.展开更多
Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) i...Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) is the maximal function on R+n+1, which was introduced by Ruiz,F. and Torrea, J.展开更多
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field...In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.展开更多
With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to ...With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.展开更多
Several new q-integral inequalities are presented. Some of them are new, One concerning double integrals, and others are generalizations of results of Miao and Qi [1]. A new key lemma is proved as well.
The aim of this present paper is to establish some new integrodifferential inequalities of Gronwall type involving functions of one independent variable which provide explicit bounds on unknown functions. The inequali...The aim of this present paper is to establish some new integrodifferential inequalities of Gronwall type involving functions of one independent variable which provide explicit bounds on unknown functions. The inequalities given here can be used in the analysis of a class of differential equations as handy tools.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as ...In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.展开更多
文摘The goal of the present paper is to establish some new approach on the basic integral inequality of Gronwall-Bellman type and its generalizations involving function of one independent variable which provides explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential and integral equations.
基金supported by the Natural Science Foundation of China(11701176,61673169,11301127,11626101,11601485)the Science and Technology Research Program of Zhejiang Educational Committee(Y201635325)
文摘We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
文摘In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.
文摘In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
文摘In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.
文摘In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.
基金The Key Scientific and Technological Innovation Team Project(2014KCT-15)in Shaanxi Province
文摘In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function.
文摘A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).
文摘The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.
文摘By using the properties of modified Riemann-Liouville fractional derivative, some new delay integral inequalities have been studied. First, we offered explicit bounds for the unknown functions, then we applied the results to the research concerning the boundness, uniqueness and continuous dependence on the initial for solutions to certain fractional differential equations.
文摘Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) is the maximal function on R+n+1, which was introduced by Ruiz,F. and Torrea, J.
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
文摘In the last years, the theory of integral inequalities are playing a very significant role in all fields of mathematics, many monographs have been devoted to this subject and present a very active and attractive field of research, the applications of integral inequalities have known a great development in many branches of mathematics in statistics, differential equations and numerical integration, The aim of this paper is to establish new extension of the weighted montgomery identity for double integrals then used it to establish new t^eby^evtype inequalities.
基金supported by the National Natural Science Foundation of China(no.51374199).
文摘With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.
文摘Several new q-integral inequalities are presented. Some of them are new, One concerning double integrals, and others are generalizations of results of Miao and Qi [1]. A new key lemma is proved as well.
文摘The aim of this present paper is to establish some new integrodifferential inequalities of Gronwall type involving functions of one independent variable which provide explicit bounds on unknown functions. The inequalities given here can be used in the analysis of a class of differential equations as handy tools.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
文摘In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
