Volume 24 , Issue 3 , PP: 233-239, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Raed Hatamleh 1 *
Doi: https://doi.org/10.54216/IJNS.240320
Uryson's operators are very famous in the theory of fuzzy functional analysis. This paper is dedicated to studying and generalizing many results about the compactness and the continuity of Uryson's operator in two-variables defined with integral equation on G with the norm
‖u‖f= sup(ρ(v,f)≤) |∫u(x)v(x)dxG | ;v(x)∈L*g ,u(x)∈Lf*.
Also, we study the convergence of Urysons' sequences Kn defined with the family of functions Kn (x, y; u) by using the convergence with respect to the defined measure and Caratheodory Condition.
Fuzzy functional analysis , Uryson's operator , Orlicz space , measure.
[1] Luxemburg W . A.J. and Zaanen A . C. :Some remarks on Banach function space , Nederl . Akad .Wetensch.Proc.ser.A.59-Indag.Math.56( 1984).
[2] Hatamleh, R., “ On the Form of Correlation Function for a Class of Nonstationary Field with a Zero Spectrum, ” Rocky Mountain Journal of Mathematics, 33(1),2003.
[ 3 ] D.L.Cohn :,Measure Theory ,Birk hauser ,Boston,p.138-212. (1980)
[4 ] D.Girela and J.A.P elaez:, Carlson Measures ,multipliers and integration operators for space of Dirichlet Type,J.Anal.Math .Malaga spain,1-15. ( 2006)
[5] Hatamleh, R., Zolotarev, V. A., “Triangular Models of Commutative Systems of Linear Operators Close to Unitary Operators, ” Ukrainian Mathematical Journal,68(5),791–811,2006.
[ 6 ] K .Hoffman :,Banach spaces of Analytic function ,Dover Publi cations, Inc, Minneola New York p.379-417, ( 2007).
[7] Heilat, A. S., Zureigat, H., Hatamleh, R., Batiha, B., “New Spline Method for Solving Linear Two-Point Boundar Value Problems,” European Journal of Pure and Applied Mathematics, 14(4), 1283–1294,2021.
[8 ] Milnes H.W. :,Convexity of Orlicz spaces,Pacif.J.Math,7.3(1957).
[9 ] H.L.Royden : Real Analysis THIRD EDITION.p.118-130,( 1988).
[10 ] WALTER RUDIN: Principles of Mathematical Analysis McGRAW-HILL INTERNATIONAL EDITIONS(Mathematics Series).p.300-325,( 1976).
[11] T.Qawasmeh,R.Hatamleh, “A new contraction based on H-simulation functions in the frame of extended b-metric spaces and application,”International Journal of Electrical and Computer Engineering, 13 (4),4212-4221,2023.
[12] Walter Rudin: FUNCTIONAL ANALYSIS McGRAW-HILL INTERNATIONAL EDITIONS(Mathematics Serie),p.292-363 . (1980).
[13] Erwin Kreyszig: INTRODUTORY FUNCTINAL ANALYSIS WITH APPLICATIONS University of Windsor,p .129-197.(1978).
[14] Ayman Hazaymeh, Rania Saadeh, Raed Hatamleh, Mohammad W Alomari, Ahmad Qazza, “A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates,” Axioms-MDPI, ,12(9),803,2023.
[15] Bayramov and C. Gunduz, “Soft locally compact spaces and soft paracompact spaces,” Journal of Mathematics and System, vol. 3, pp. 122–130, 2013.
[16] S. Das and S. K. Samanta, “Soft Metric,” Annals of Fuzzy Mathematics and Informatics, vol. 6, no. 1, pp. 77–94, 2013.
[17] M. I. Yazar, T. Bilgin, S. Bayramov, and C. Gunduz (Aras), “A new view on soft normed spaces,” International Mathematical Forum, vol. 9, no. 24, pp. 1149–1159, 2014.
[18] Hatamleh, R., Zolotarev, V. A., “On Two-Dimensional Model Representations of One Class of Commuting Operators, ” Ukrainian Mathematical Journal, 66(1), 122–144,2014.
[19] S. Das and S. K. Samanta, “On soft inner product spaces,” Annals of Fuzzy Mathematics and Informatics, vol. 6, no. 1, pp. 151–170, 2013.
[20] Hatamleh, R., & Zolotarev, V. A., “ On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component, ” Zurnal Matematiceskoj Fiziki, Analiza, Geometrii, 11(2), 174–186,2015.
[21] Ayman Hazaymeh, Ahmad Qazza, Raed Hatamleh, Mohammad W Alomari, Rania Saadeh, “On Further Refinements of Numerical Radius, Inequalities,” Axiom-MDPI, 12(9),807,2023.
