泛函积分Cauchy中值定理“中间点”的渐近性
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摘要
利用比较函数,在赋范线性空间中研究积分Cauchy中值定理"中间点"的渐近性态,在一定条件下建立了泛函积分Cauchy中值定理"中间点"的更为广泛的渐近估计式.获得的结果推广和改进了相关文献中的相应结果.
The asymptotic behavior of the intermediate point for integrals Cauchy mean value theorem in normed linear spaces was studied by using the concept of comparison function, and several new asymptotic estimation formulas for functional integrals Cauchy mean value theorem were established under certain conditions. The results were obtained to extend and improve the corresponding results of some reference.
The asymptotic behavior of the intermediate point for integrals Cauchy mean value theorem in normed linear spaces was studied by using the concept of comparison function, and several new asymptotic estimation formulas for functional integrals Cauchy mean value theorem were established under certain conditions. The results were obtained to extend and improve the corresponding results of some reference.
引文
[1] AZPEITJA A G.On the Lagrange remainder of the Taylor formula[J].The American Mathematical Monthly,1982,89(5):311-312.
[2] JACOBSON B.On the mean value theorem for integrals[J].The American Mathematical Monthly,1982,89(5):300-301.
[3] 张树义.关于“中间点”渐近性的两个结果[J].辽宁师范大学学报(自然科学版),1995,18(2):109-111.ZHANG S Y.Two results on the asymptotic behavior of “intermediate point”[J].Journal of Liaoning Normal University(Natural Science Edition),1995,18(2):109-111.
[4] REN L S,ZHANG C Y.The asymptotic property of generalized Taylor remainder “mean value point”[J].Chinese Quarterly Journal of Mathematics,2004,19(3):314-318.
[5] 任立顺.关于泛函积分“中值点”的渐近值[J].周口师范学院学报(自然科学版),2003,20(5):1-4.REN L S.On the asymptotic value of “median point” in functional integral[J].Journal of Zhoukou Normal University(Natural Science Edition),2003,20(5):1-4.
[6] 刘丽娜.泛函积分Cauchy中值定理及其逆问题[J].高等数学研究,2017,17(4):27-30.LIU L N.Cauchy mean value theorem of functional integral and its inverse problem[J].Studies in College Mathematics,2017,17(4):27-30.
[7] 张树义,丛培根,张芯语.泛函Taylor公式“中间点”的渐近性[J].烟台大学学报(自然科学与工程版),2018,31(3):189-192.ZHANG S Y,CONG P G,ZHANG X Y.Asymptotic behavior of the “ntermediate point” for functional Taylor formula[J].Journal of Yantai University(Natural Science and Engineering Edition) ,2018,31(3):189-192.
[8] 张树义.广义Taylor公式“中间点”一个更广泛的渐近估计式[J].数学的实践与认识,2004,34(11):173-176.ZHANG S Y.A more extensive asymptotic estimation formulas of the “intermediate point” in the generalized Taylor formula[J].Mathematics in Practice and Theory,2004,34(11):173-176.
[9] 林媛,张树义.广义泰勒中值定理“中间点"当x→+∞时更广泛的渐近估计式[J].南阳师范学院学报(自然科学版),2016(3):1-5.LIN Y,ZHANG S Y.More extensive asymptotic estimation formula of the“intermediate point”for generalized Taylor mean value theorem when x is near+∞[J].Journal of Nanyang Normal University(Natural Science Edition),2016(3):1-5.
[10] 刘冬红,张树义,丛培根.积分中值定理中间点函数的性质[J].北华大学学报(自然科学版),2017,18(4):434-438.LIU D H,ZHANG S Y,ZHENG X D.Properties of intermediate point function for integrals mean value theorem[J].Journal of Beihua University(Natural Science Edition),2017,18(4):434-438.
[11] 万美玲,张树义.二元函数Taylor公式“中间点”的渐近估计式[J].鲁东大学学报(自然科学版),2016,32(2):1-4.WAN M L,ZHANG S Y.Asymptotic estimation formulas of the “intermediate point” in the Taylor mean value formula for two variable functions[J].Journal of Ludong University(Natural Science Edition) ,2016,32(2):1-4.
[12] 张树义,赵美娜,郑晓迪.积分中值定理中间点的渐近估计式[J].北华大学学报(自然科学版),2016,17(4):448-454.ZHANG S Y,ZHAO M N,ZHENG X D.Asymptotic estimation formulas of the “intermediate point” for integral mean value theorem[J].Journal of Beihua University(Natural Science Edition),2016,17(4):448-454.
[13] 赵美娜,张树义,郑晓迪.广义Taylor中值定理“中间点函数”的性质[J].南通大学学报(自然科学版),2016,15(3):80-85.ZHAO M N,ZHANG S Y,ZHENG X D.Properties of “intermediate point function” for generalized Taylor mean value theorem[J].Journal of Nantong University(Natural Science Edition),2016,15(3):80-85.
[14] 刘冬红,张树义,郑晓迪.二元函数柯西中值定理“中间点”的渐近估计式[J].井冈山大学学报(自然科学版),2017,38(4):13-17.LIU D H,ZHANG S Y,ZHENG X D.Asymptotic estimation formula of the “intermediate point” in the Cauchy mean value theorem for two variable functions[J].Journal of Jinggangshan University(Natural Science Edition) ,2017,38(4):13-17.
[15] 张树义,丛培根,郑晓迪.高阶Cauchy中值定理中间点函数的性质[J].北华大学学报(自然科学版),2017,18(1):19-24.ZHANG S Y,CONG P G,ZHENG X D.Properties of intermediate point function for high order Cauchy mean value theorem[J].Journal of Beihua University(Natural Science Edition),2017,18(1):19-24.
[16] 张芯语,张树义.关于广义Taylor中值定理“中间点函数”可微性的进一步讨论[J].井冈山大学学报(自然科学版),2018,39(2):5-13.ZHANG X Y,ZHANG S Y.Further discuss on differentiability of intermediate point function for generalized Taylor mean value theorem[J].Journal of Jinggangshan University(Natural Science Edition),2018,39(2):5-13.
[17] 张树义,林媛,郑晓迪.广义中值定理中间点函数的性质[J].北华大学学报(自然科学版),2016,17(6):714-719.ZHANG S Y,LIN Y,ZHENG X D.Properties of intermediate point function for generalized mean value theorem[J].Journal of Beihua University(Natural Science Edition) ,2016,17(6):714-719.
[18] 丛培根,张树义.关于高阶Cauchy中值定理中间点函数可微性的进一步研究[J].南通大学学报(自然科学版),2018,17(1):90-94.CONG P G,ZHANG S Y.Further study on differentiability of intermediate point function for high order Cauchy mean value theorem[J].Journal of Nantong University(Natural Science Edition),2018,17(1):90-94.
[19] POWERS R C,RIEDEL T,SAHOO P K.Limit properties of differential mean values[J].Journal of Mathematical Analysis & Applications,1998,227(1):216-226.
[20] DUCA D I,POP O.On the intermediate point in Cauchy's mean-value theorem[J].Mathematical Inequalities & Applications,2006,9(3):375-389.
[21] 钟承奎,范先令,陈文塬.非线性泛函分析引论[M] .兰州:兰州大学出版社,1998.ZHONG C K,FAN X L,CHEN W Y.Nonlinear functional analysis guide[M].Lanzhou:Lanzhou University Press,1998.
[2] JACOBSON B.On the mean value theorem for integrals[J].The American Mathematical Monthly,1982,89(5):300-301.
[3] 张树义.关于“中间点”渐近性的两个结果[J].辽宁师范大学学报(自然科学版),1995,18(2):109-111.ZHANG S Y.Two results on the asymptotic behavior of “intermediate point”[J].Journal of Liaoning Normal University(Natural Science Edition),1995,18(2):109-111.
[4] REN L S,ZHANG C Y.The asymptotic property of generalized Taylor remainder “mean value point”[J].Chinese Quarterly Journal of Mathematics,2004,19(3):314-318.
[5] 任立顺.关于泛函积分“中值点”的渐近值[J].周口师范学院学报(自然科学版),2003,20(5):1-4.REN L S.On the asymptotic value of “median point” in functional integral[J].Journal of Zhoukou Normal University(Natural Science Edition),2003,20(5):1-4.
[6] 刘丽娜.泛函积分Cauchy中值定理及其逆问题[J].高等数学研究,2017,17(4):27-30.LIU L N.Cauchy mean value theorem of functional integral and its inverse problem[J].Studies in College Mathematics,2017,17(4):27-30.
[7] 张树义,丛培根,张芯语.泛函Taylor公式“中间点”的渐近性[J].烟台大学学报(自然科学与工程版),2018,31(3):189-192.ZHANG S Y,CONG P G,ZHANG X Y.Asymptotic behavior of the “ntermediate point” for functional Taylor formula[J].Journal of Yantai University(Natural Science and Engineering Edition) ,2018,31(3):189-192.
[8] 张树义.广义Taylor公式“中间点”一个更广泛的渐近估计式[J].数学的实践与认识,2004,34(11):173-176.ZHANG S Y.A more extensive asymptotic estimation formulas of the “intermediate point” in the generalized Taylor formula[J].Mathematics in Practice and Theory,2004,34(11):173-176.
[9] 林媛,张树义.广义泰勒中值定理“中间点"当x→+∞时更广泛的渐近估计式[J].南阳师范学院学报(自然科学版),2016(3):1-5.LIN Y,ZHANG S Y.More extensive asymptotic estimation formula of the“intermediate point”for generalized Taylor mean value theorem when x is near+∞[J].Journal of Nanyang Normal University(Natural Science Edition),2016(3):1-5.
[10] 刘冬红,张树义,丛培根.积分中值定理中间点函数的性质[J].北华大学学报(自然科学版),2017,18(4):434-438.LIU D H,ZHANG S Y,ZHENG X D.Properties of intermediate point function for integrals mean value theorem[J].Journal of Beihua University(Natural Science Edition),2017,18(4):434-438.
[11] 万美玲,张树义.二元函数Taylor公式“中间点”的渐近估计式[J].鲁东大学学报(自然科学版),2016,32(2):1-4.WAN M L,ZHANG S Y.Asymptotic estimation formulas of the “intermediate point” in the Taylor mean value formula for two variable functions[J].Journal of Ludong University(Natural Science Edition) ,2016,32(2):1-4.
[12] 张树义,赵美娜,郑晓迪.积分中值定理中间点的渐近估计式[J].北华大学学报(自然科学版),2016,17(4):448-454.ZHANG S Y,ZHAO M N,ZHENG X D.Asymptotic estimation formulas of the “intermediate point” for integral mean value theorem[J].Journal of Beihua University(Natural Science Edition),2016,17(4):448-454.
[13] 赵美娜,张树义,郑晓迪.广义Taylor中值定理“中间点函数”的性质[J].南通大学学报(自然科学版),2016,15(3):80-85.ZHAO M N,ZHANG S Y,ZHENG X D.Properties of “intermediate point function” for generalized Taylor mean value theorem[J].Journal of Nantong University(Natural Science Edition),2016,15(3):80-85.
[14] 刘冬红,张树义,郑晓迪.二元函数柯西中值定理“中间点”的渐近估计式[J].井冈山大学学报(自然科学版),2017,38(4):13-17.LIU D H,ZHANG S Y,ZHENG X D.Asymptotic estimation formula of the “intermediate point” in the Cauchy mean value theorem for two variable functions[J].Journal of Jinggangshan University(Natural Science Edition) ,2017,38(4):13-17.
[15] 张树义,丛培根,郑晓迪.高阶Cauchy中值定理中间点函数的性质[J].北华大学学报(自然科学版),2017,18(1):19-24.ZHANG S Y,CONG P G,ZHENG X D.Properties of intermediate point function for high order Cauchy mean value theorem[J].Journal of Beihua University(Natural Science Edition),2017,18(1):19-24.
[16] 张芯语,张树义.关于广义Taylor中值定理“中间点函数”可微性的进一步讨论[J].井冈山大学学报(自然科学版),2018,39(2):5-13.ZHANG X Y,ZHANG S Y.Further discuss on differentiability of intermediate point function for generalized Taylor mean value theorem[J].Journal of Jinggangshan University(Natural Science Edition),2018,39(2):5-13.
[17] 张树义,林媛,郑晓迪.广义中值定理中间点函数的性质[J].北华大学学报(自然科学版),2016,17(6):714-719.ZHANG S Y,LIN Y,ZHENG X D.Properties of intermediate point function for generalized mean value theorem[J].Journal of Beihua University(Natural Science Edition) ,2016,17(6):714-719.
[18] 丛培根,张树义.关于高阶Cauchy中值定理中间点函数可微性的进一步研究[J].南通大学学报(自然科学版),2018,17(1):90-94.CONG P G,ZHANG S Y.Further study on differentiability of intermediate point function for high order Cauchy mean value theorem[J].Journal of Nantong University(Natural Science Edition),2018,17(1):90-94.
[19] POWERS R C,RIEDEL T,SAHOO P K.Limit properties of differential mean values[J].Journal of Mathematical Analysis & Applications,1998,227(1):216-226.
[20] DUCA D I,POP O.On the intermediate point in Cauchy's mean-value theorem[J].Mathematical Inequalities & Applications,2006,9(3):375-389.
[21] 钟承奎,范先令,陈文塬.非线性泛函分析引论[M] .兰州:兰州大学出版社,1998.ZHONG C K,FAN X L,CHEN W Y.Nonlinear functional analysis guide[M].Lanzhou:Lanzhou University Press,1998.