Abstract
We establish some newn-independent-variable discrete inequalities which are analogous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author inJ. Math. Anal. Appl., 109 (1985), 171–181. An application to hyperbolic summary-difference equations inn variables is also sketched.
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References
Agarwal, R.P., Sharp estimate for the Wendroff discrete inequalities inn-independent variables. An. Sti. Univ.Al.I.Cuza Iasi, (N.S.) Sect. I a Mat.,30(1984), 65–68.
Beesack, P.R., Lower bounds from discrete inequalities of Gollwitzer-Langenhop type, An. Sti. Univ.Al.I.Cuza Iasi, (N.S.) Sect.I a Mat.,30(1984), 25–30.
Bondge,B.K. andPachpatte,B.G.,On some fundamental integral inequalities in two independent variables,J.Math.Anal.Appl. 72(1979), 533–544.
Dannan, F.M., Submultiplicative and subadditive functions and integral inequalities of Bellman-Bihari type,J.Math.Anal. Appl.,120(1986), 631–646.
Gollwitzer, H.E., A note on a functional inequality,Proc.Amer.Math.Soc.,23(1969), 542–547.
Langenhop, C.E., Bounds on the norm of a solution of a general differential equation,Proc.Amer.Math.Soc.,11(1960), 795–799.
Pachpatte, B.G., A note on integral inequalities of the Bellman-Bihari type,J. Math. Anal. Appl.,49(1975), 295–301.
Pachpatte, B.G., A note on integral inequality.J. Math. Phys.Sci.,9(1975), 11–14.
Pachpatte, B.G., On some fundamental discrete inequalities in two independent variables,Tamkang J. Math.,12(1981), 21–33.
Pachpatte, B.G., and Singare, S.M., Discrete generalized inequalities in three independent variables,Pacif.J.Math.,82(1979),192–210.
Shih, M.H. and Yeh, C.C., Some integral inequalities inn independent variables,J. Math. Anal. Appl.,84(1981), 569–583.
Singare, S.M., and Pachpatte, B.G., Wendroff type discrete inequalities nd their applications,J.Math.Phys. Sci.Madras,13(1979), 149–167.
Singare, S.M. and Pachpatte, B.G., On certain discrete inequalities of the Wendroff type,Indian J. Pure Appl. Math.,11(1980), 727–736.
Singare, S.M. and Pachpatte, B.G., On some fundamental discrete inequalities of the Wendroff type, An.Sti.Univ.Al.I.Cuza Iasi, (N.S.) Sect.I a Mat.,26(1980), 85–94.
Yang Enhao, On some new integral inequalities inN independent variables,J. Math. Anal. Appl.,109(1985), 171–181.
Yang Enhao, On some newn-independent-variable discrete inequalities of the Gronwall type,Int. J. Math. & Math. Sci.,9(1986), 485–495.
Yeh, C.C., Discrete inequalities of the Gronwall-Bellman type inn independent variables,J. Math. Anal. Appl.,105(1985), 322–332.
Yeh, C.C., Discrete inequalities of the Gronwall-Bellman type inn independent variables, II,J. Math. Anal. Appl.,106(1985), 282–285.
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Enhao, Y. Discrete generalizations of someN-independent-variable integral inequalities of Langenhop-Gollwitzer type. Acta Mathematica Sinica 6, 230–242 (1990). https://doi.org/10.1007/BF02108202
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DOI: https://doi.org/10.1007/BF02108202