基于区间值测度伪积分的Barnes-Godunova-Levin型和Lyapunov型不等式（英文）
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摘要
本文首先证明了伪积分的Barnes-Godunova-Levin型不等式以及实值函数区间值测度伪积分的Barnes-Godunova-Levin型不等式.随后证明了两种不同区间值测度伪积分的Lyapunov型不等式.其中一种是基于区间值函数的伪积分,另一种是基于实值函数的伪积分.
In this paper,firstly we focus on Barnes-Godunova-Levin type inequalities for pseudo-integral and Barnes-Godunova-Levin type inequality for interval-valued measure via pseudo-integral of real valued function.Then Lyapunov type inequality for pseudo-integrals with respect to two interval-valued measure is proved.One is defined by the pseudo-integral of interval-valued function,the other one obtained through pseudo-integrals of real-valued functions.
In this paper,firstly we focus on Barnes-Godunova-Levin type inequalities for pseudo-integral and Barnes-Godunova-Levin type inequality for interval-valued measure via pseudo-integral of real valued function.Then Lyapunov type inequality for pseudo-integrals with respect to two interval-valued measure is proved.One is defined by the pseudo-integral of interval-valued function,the other one obtained through pseudo-integrals of real-valued functions.
引文
[1]Grbic T,Medic S,Stajner-Papuga I and DoSenovic T.Intelligent Systems:Models and Applications.Intelligent Systems and Informatics.2013.
[2]Medic S,Grbic T,Perovic A and Nikolicic S.Inequalities of Holder and Minkowski type for Pseudointegrals with respect to Interval-valued(?)-measures.Fuzzy Sets Syst.,Accept.
[3]Grbic T,Stajner-Papuga I and Strboja M.An Approach to Pseudo-integration of Set-valued Functions.Inf.Sci.,2011,181:2278-2292.
[4]Flores-Franulic A,Roman-Flores H and Chalco-Cano Y.Markov Type Inequalities for Fuzzy Integrals.Appl.Math.Comput.,2009,207:242-247.
[5]Grbic T,Stajner-Papuga I nad Nedovic L.Pseudo-integral of Set-valued Functions.Vol.I.,2007:221-225.
[6]u L,Sun J,Ye X and Zhu L.Holder Type Inequality for Sugeno Integrals.Fuzzy Sets Syst.,2010,161(1):2337-2347.
[7]L.C.J.A Note on the Pseudo Stolarsky Type Inequality for the g-integral.Appl.Math.Comput.,2015,269:809-815.
[8]L.C.J.Some Properties of the Interval-valued g-integrals and a Standard Interval-valueds-integral.J.Inequal.Appl,2014,88:1186-1029.
[9]Li L S and Sheng Z H.The Fuzzy Set-valued Measures Generated by Random Variables.Fuzzy Sets Syst.,1998,97:203-209.
[10]Schjaer-Jacobsen H.Representation and Calculation of Economic Uncertainties:Intervals Fuzzy Numbers,and Probabilities.Int.J.Prod.Econ.,2002,78:91-98.
[11]Weichselberger K.The Theory of Interval-probability as a Unifying Concept for Uncertainty.Int.J.Approx.Reas.,2000,24:149-170.
[12]Mesiar R and Pap E.Idempotent Integral as Limit of g-integrals.Fuzzy.Sets.Syst.,1999,102:385-392.
[13]Sugeno M.Theory of Fuzzy Integrals and it's Applications.Tokyo:Institute of Technology,1974.
[14]Pap E.Generalization Real Analysis and its Applications.Int.J.Approximate.Reasoning.2008,47:368-386.
[15]Sugeno M and Murofushi T.Pseudo-additive Measure and Integrals.J.Math.Anal.Appl.,1987,122:197-222.
[16]Agahi H,Mesiar R and Ouyang Y.Chebyshev type Inequalities for Pseudo-integrals.Nonlinear Anal.,2010,72:2737-2743.
[17]Agahi H,Ouyang Y,Mesiar R,Pap E and Strboja M.H(o|¨)der and Minkowski Type Inequalities for Pseudo-integrals.Appl.Math.Comput.,2011,217:8630-8639.
[18]Daraby B.Generalization of the Stolarsky Type Inequalities for Pseudo-integrals.Fuzzy.Sets.Syst.2012,194:90-96.
[19]Pap E and Strboja M.Generalization of the Jensen Type Inequalities for Pseudo-integrals.Inf.Sci.,2010,180:543-548.
[20]Li D Q,Song X Q,Yue T and Song Y Z.Generalization of the Lyapunov Type Inequalities for Pseudo-integrals.Appl.Math.Comput.,2014,241:64-69.
[21]Agahi H,Roman-Flores H and Flores-Franulic A.General Baxnes-Godunova-Levin Type Inequality for Fuzzy Integrals.Inf.Sci.,2011,181:1072-1079.
[22]Anastassion G.Chebyshev Grass Type Inequalities for Fuzzy Integrals.Appl.Math.Comput.,2007,45:1189-1200.
[23]Li D Q,Song X Q and Yue T.Hermite-Hadamard Type Inequality for Sugeno Integrals.Appl.Math.Comput.,2014,237:632-638.
[24]Yng X L,Song X Q and Lu W.Sandor's Type Inequality for Fuzzy Integrals.Journal of Nanjing University:Mathematical Biquarterly,2015,32(2):144-156.
[25]Song Y Z,Song X Q,Li D Q and Yue T.Berwald Type Inequality for Extremal Universal Integral based on(a,m)-concave Functions.J.Math.Inequal,2015,9(1):1-15.
[26]Song X Q and Pan Z.Fuzzy Algebra in Triangular norm System.Fuzzy Sets Syst.,1998,93(3):331-335.
[27]Pecaric J E,Proschan F and Tong Y L.Convex Functions,Partical Orderings,and Statistical Applications.Academic Press Inc.,Boston-San Diego-New York,1992.
[2]Medic S,Grbic T,Perovic A and Nikolicic S.Inequalities of Holder and Minkowski type for Pseudointegrals with respect to Interval-valued(?)-measures.Fuzzy Sets Syst.,Accept.
[3]Grbic T,Stajner-Papuga I and Strboja M.An Approach to Pseudo-integration of Set-valued Functions.Inf.Sci.,2011,181:2278-2292.
[4]Flores-Franulic A,Roman-Flores H and Chalco-Cano Y.Markov Type Inequalities for Fuzzy Integrals.Appl.Math.Comput.,2009,207:242-247.
[5]Grbic T,Stajner-Papuga I nad Nedovic L.Pseudo-integral of Set-valued Functions.Vol.I.,2007:221-225.
[6]u L,Sun J,Ye X and Zhu L.Holder Type Inequality for Sugeno Integrals.Fuzzy Sets Syst.,2010,161(1):2337-2347.
[7]L.C.J.A Note on the Pseudo Stolarsky Type Inequality for the g-integral.Appl.Math.Comput.,2015,269:809-815.
[8]L.C.J.Some Properties of the Interval-valued g-integrals and a Standard Interval-valueds-integral.J.Inequal.Appl,2014,88:1186-1029.
[9]Li L S and Sheng Z H.The Fuzzy Set-valued Measures Generated by Random Variables.Fuzzy Sets Syst.,1998,97:203-209.
[10]Schjaer-Jacobsen H.Representation and Calculation of Economic Uncertainties:Intervals Fuzzy Numbers,and Probabilities.Int.J.Prod.Econ.,2002,78:91-98.
[11]Weichselberger K.The Theory of Interval-probability as a Unifying Concept for Uncertainty.Int.J.Approx.Reas.,2000,24:149-170.
[12]Mesiar R and Pap E.Idempotent Integral as Limit of g-integrals.Fuzzy.Sets.Syst.,1999,102:385-392.
[13]Sugeno M.Theory of Fuzzy Integrals and it's Applications.Tokyo:Institute of Technology,1974.
[14]Pap E.Generalization Real Analysis and its Applications.Int.J.Approximate.Reasoning.2008,47:368-386.
[15]Sugeno M and Murofushi T.Pseudo-additive Measure and Integrals.J.Math.Anal.Appl.,1987,122:197-222.
[16]Agahi H,Mesiar R and Ouyang Y.Chebyshev type Inequalities for Pseudo-integrals.Nonlinear Anal.,2010,72:2737-2743.
[17]Agahi H,Ouyang Y,Mesiar R,Pap E and Strboja M.H(o|¨)der and Minkowski Type Inequalities for Pseudo-integrals.Appl.Math.Comput.,2011,217:8630-8639.
[18]Daraby B.Generalization of the Stolarsky Type Inequalities for Pseudo-integrals.Fuzzy.Sets.Syst.2012,194:90-96.
[19]Pap E and Strboja M.Generalization of the Jensen Type Inequalities for Pseudo-integrals.Inf.Sci.,2010,180:543-548.
[20]Li D Q,Song X Q,Yue T and Song Y Z.Generalization of the Lyapunov Type Inequalities for Pseudo-integrals.Appl.Math.Comput.,2014,241:64-69.
[21]Agahi H,Roman-Flores H and Flores-Franulic A.General Baxnes-Godunova-Levin Type Inequality for Fuzzy Integrals.Inf.Sci.,2011,181:1072-1079.
[22]Anastassion G.Chebyshev Grass Type Inequalities for Fuzzy Integrals.Appl.Math.Comput.,2007,45:1189-1200.
[23]Li D Q,Song X Q and Yue T.Hermite-Hadamard Type Inequality for Sugeno Integrals.Appl.Math.Comput.,2014,237:632-638.
[24]Yng X L,Song X Q and Lu W.Sandor's Type Inequality for Fuzzy Integrals.Journal of Nanjing University:Mathematical Biquarterly,2015,32(2):144-156.
[25]Song Y Z,Song X Q,Li D Q and Yue T.Berwald Type Inequality for Extremal Universal Integral based on(a,m)-concave Functions.J.Math.Inequal,2015,9(1):1-15.
[26]Song X Q and Pan Z.Fuzzy Algebra in Triangular norm System.Fuzzy Sets Syst.,1998,93(3):331-335.
[27]Pecaric J E,Proschan F and Tong Y L.Convex Functions,Partical Orderings,and Statistical Applications.Academic Press Inc.,Boston-San Diego-New York,1992.