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Abstract
In this study we present the existence and uniqueness of a non-homogeneous second order difference equation of accretive type in linear 2-Banach spaces. We use the 2-norm contraction mapping and its fixed point to establish our results.
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References
C. K. Sari, Some Properties of m-accretive Operators in Normed Spaces, International Conference on Science, Technology and Humanity 2015, ISSN 2477-3328.
V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces. The Netherlands, 1976.
J. Garcia-Falset, S. Reich. Zeroes of Accretive Operators and the Asymptotic Behaviour of Nonlinear Semigroups. Houston Journal of Mathematics, Vol. 32, No. 04, 1197-1223, 2006.
J. S. Jung. Strong Convergence of an Iterative Algorithm for Accretive Operators and Nonexpansive Mappings, Journal of oj Nonlinear Science and Application Vol.9,000-000, 2016.
B. D. Rouhani, P. Jamshidnezhad, and S. Saeidi, Zeros of accretive op- erators and asymptotics of a second order di erence inclusion in banach spaces, Journal of Mathematical Analysis and Applications, vol. 480, no. 2, p. 123428, 2019.
N.C. Apreutesei. Existence and Asymptotic Behaviour for Some Difference Equations Associated with Accretive Operators. V. Barbu (eds.). Analysis and Optimization of Differential System. International Federation for Information Processing, 2003.
B. D. Rouhani, P. Jamshidnezhad, S. Saeidi. Zeros of Accretive Operators and ASymptotics of a Second Order Difference Inclusion in Banach Spaces. J. of Math. Anal. Appl. 480, 123428, 2019.
B. D. Rouhani, H. Khatibzadeh. New Results on the Asymptotic Behaviour of Solutions to a Class of Second Order Nonhomogeneous Difference Equations. Nonlinear Analysis, Vol.74, 5727-5734, 2011.
G. Apreutesei; N. Apreutesei. Second Order Difference Inclusions of Monotone Type. Mathematica, Vol.137, No.2,123-130,2012.
P. Jamshidnezhad and S. Saeidi, On Nonhomogeneous Second Order Difference Inclusions of Accretive Type in Banach Spaces, Numerical Functional Analysis and Optimization, Vol. 39 No. 8, 894-920, 2018.
M. Kir. A New Approach to Accretive Operators Arsing from 2-Banach Spaces. Gen. Math. Notes Vol.16 No.2, 48-54, 2013.
P. K Harikrishnan and K. T. Ravindran, Some Properties of Accretive Operators in Linear 2-Normed Spaces. International Mathematical Forum, Vol.6, No.59, 2941-2941, 2011.
M. E. Hryrou and S. Kabbaj. On a Generalized Drygas Functional Equation and its Approximate Solutions in 2-Banach Spaces. Kragujevac Journal of Mathematics. Vol. 47, No. 5, 801-S 815, 2023.
K. V. N. Sayar and A. Bergam. Stability of Cauchy-Jensen Type Functional Equation in (2,α)-Banach Spaces. Kragujevac Journal of Mathematics. Vol.46, No.6, 905-017, 2022.
M. Gurdal, A. Sahiner, I. Acik.Approximation Theory in 2-Banach Spaces. Nonlinear Analysis, Vol.71, 1654-1661, 2009.
S. S. Abed, R. S. Abed-Ali. Fixed Point for Asyptotically Non-Expansive Mappings in 2-Banach Space. Ibn Al-Haitham Journal for Pure and Applied Science, Vol.27, No. 1, 343-250, 2014.
C. S. Lin. On Strictly Convex and Strictly 2-Convex 2-Normed Spaces II. International Journal of Mathematics and Mathematical Sciences, Vol.15, No.3, 417-424, 1992.
K. Iseki. Mathematics on Two Normed Spaces. Bull-Koeran Mathematical V. Barbu. Nonlinear Differential Equations of Monotone Types in Banach Spaces. Springer Monograghs in Mathematics, 2010.