FIXED POINTS OF A NONHOMOGENIOUS SECOND ORDER DIFFERENCEEQUATION OF ACCRETIVE TYPE IN HILBERT SPACES

James T Pember; Ibrahim Garba Bassi; G. T. Gyegwe

doi:10.62050/fjst2026.v10n2.740

المؤلفون

James T Pember
pemberjames90@gmail.com

Nasarawa State University, Keffi, Nigeria
Ibrahim Garba Bassi
Federal University of Lafia, Nigeria
G. T. Gyegwe
National Teachers’ Institute, Lafia, Nigeria

الكلمات المفتاحية:

Accretive operator , Hilbert spaces , Parallelogram law , Norm spaces , Inner product

الملخص

In this study, we establish the existence of a common fixed point in a nonhomogeneous second order difference equation of accretive type in Hilbert spaces. We used a contraction and rational inequality in Hilbert spaces to obtain our result and its uniqueness.

السير الشخصية للمؤلفين

James T Pember

Department of Mathematics

Ibrahim Garba Bassi

Department of Mathematics

G. T. Gyegwe

Department of Mathematics

Dimensions

REFERENCES

Appreutesei, N. (2003). Existence and Asymptotic Behaviour for Some Difference Equations Associated with Accretive Operators. Technical University of Iasic.

Apreutesei, N. C. (1998). Second-order differential equations on half-line associated with monotone operators. Journal of Math. Anal. Appl., 223, 472-493.

Apreutesei, G. and Apreutesei, N. (2012). Second order difference inclusions of monotone type. Mathematica Bohemica, 137(2), 123-130.

Barbu, V. (1976). Nonlinear Semigroups and Differential Equations is Banach Spaces. Noordhoff in International Publishing, Leyden, the Netherlands.

Benharrat, M. (2020). A Perturbation Result of M-accretive Linear Operators in Hilbert Spaces arXiv: 2007.13361v1[math.FA].

Debnath, L. and Mikusinski, P. (2005). Introduction to Hilbert Spaces with Applications, 3rd Edition. Elsevier Academic Press.

Garcia-Falset, J. and Morales, C. H. (2005). Existence theorems for M-accretive operators in Banach spaces. J. Math. Anal. Appl., 309, 453-461.

Jamshidnezhad, P. and Saeidi, S. (2018). On nonhomogeneous second order difference inclusions of accretive type in Banach spaces. Num. Functional Anal. and Opt., 38(8) 894-920.

Khatibzdeh, H. (2012). Convergence of solutions a second order difference inclusion. Nonlinear Analysis, 75, 3503-3509.

Rouhani, B. D. and Khatibzdeh, H. (2012). On the convergence of solutions to a second order difference equation with monotone operator. Numerical Functional Analysis and Optimization, 32(1), 1271-1282.

Luca, C. (2017). Why do we need Hilbert spaces? Department of Physics, University of Trieste, Strad Costiera II 34151, Trieste, Italy.arXiv: 708.08326vI

Moosavi, B. and Hosseini, M. S. (2024). Some norm inequalities for accretive Hilbert space operator. CUBO, A Mathematical Journal, 26(2) 327-340. D01: 10.56754/0719-2602.327.

Poffald, E. I. and Reich, S. (1986). An Incomplete Cauchy Problem. J. of Math. Anal. and Appl., 113, 14-543.

Rousan, K. A. (2023). Introduction to Hilbert space and it’s brief description in quantum mechanics. ResearchGate (pp. 1–22). Available at: https://www.researchate.net/publication/345863644_introduction_to_Hilbert_Space_and_it%27s_brief_description_in_Quantum_Mechanics

Sari, C. K. (2015). Some properties of m-accretive operators in Normed spaces. In Book of Proceeding (pp. 198–205): Int. Conference on Science, Technology and Humanity. Available at: https://proceedings.ums.ac.id/iseth/article/downdoad/2393/2348/2424

Tesch, G. (2019). Topics in Real and Functional Analysis. American Mathematical Society Providence, Rhode Island, USA.