İteratif Yaklaşım Altında Bir Fonksiyonel-İntegral Denklem Sınıfının Çözümünün İncelenmesi

Bu çalışmada üç adımlı bir sabit nokta iterasyon algoritması kullanılarak fonksiyonel-integral denklem sınıfının çözümüne ulaşılabildiği gösterilmiştir. Ayrıca bu integral denklem için veri bağlılığı sonucu elde edilmiş olup, bu sonucu destekleyen bir örnek verilmiştir

Anahtar Kelimeler:

İterasyon algoritması, fonksiyonel-integral denklem, yakınsaklık, veri bağlılığı

Examination of the Solution of A Class of Functional-Integral Equation Under Iterative Approach

In this study, it has been shown that the solution of a class of functional-integral equation can be reached by using a three-step fixed point iterative algorithm. In addition, the data dependence result for this integral equation has been obtained and in order to support this result an example has been given.

Keywords:

Iterative algorithm, functional-integral equation, convergence, data dependence,

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Atalan Y, Karakaya V, 2017. Iterative Solution of Functional Volterra-Fredholm Integral Equation with Deviating Argument. Journal of Nonlinear and Convex Analysis, 18(4): 675-684.
Atalan Y, 2018. Yeni Bir İterasyon Yöntemi İçin Hemen-Hemen Büzülme Dönüşümleri Altında Bazı Sabit Nokta Teoremleri. Marmara Fen Bilimleri Dergisi, 30(3): 276-285.
Appell J, Kalitvin A.S, 2006. Existence results for integral equations: Spectral methods vs. Fixed point theory. Fixed Point Theory, 7(2): 219-234.
Berinde V, 2010. Existence and Approximation of Solutions of Some First Order İterative Differential Equations. Miskolc Math. Notes, 11(1): 13-26.
Chugh R, Kumar V, Kumar S, 2012. Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces, Amer. J. Comput. Math., 2 (04): 345-357.
Dobritoiu M, 2008. System of Integral Equations with Modified Argument. Carpathian J. Math, 24(2): 26-36.
Gürsoy F, 2016. A Picard-S Iterative Method for Approximating Fixed Point of Weak-Contraction Mappings, Filomat, 30(10): 2829-2845.
Ishikawa S, 1974. Fixed Points by a New Iteration Method, Proc. Amer. Math. Soc., 44(1): 147-150.
Karakaya V, Atalan Y, Dogan K, Bouzara NEH, 2017. Some Fixed Point Results for a New Three Steps Iteration Process in Banach Spaces, Fixed Point Theory, 18(2): 625-640.
Khuri S.A, Sayfy,A, 2015. A Novel Fixed Point Scheme: Proper Setting Of Variational İteration Method for BVPs. Appl. Math. Lett, 48: 75-84.
Lauran M, 2011. Existence Results for Some Differential Equations with Deviating Argument. Filomat, 25(2): 21-31.
Mann W.R, 1953. Mean Value Methods in Iteration. Proc. Amer. Math. Soc., 4(3): 506-510.
Noor M.A, 2000. New Approximation Schemes for General Variational Inequalities, J. Math. Anal. Appl., 251: 217-229.
Pascale E De, Zabreiko P.P, 2004. Fixed Point Theorems for Operators in Spaces of Continuous Functions. Fixed Point Theory, 5(1): 117-129.
Petrusel A, Rus I, 2018. A Class of Functional-Integral Equations via Picard Operator Technique. Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications, 10(1): 15-24.
Phuengrattana W, Suantai S, 2011. On the Rate of Convergence of Mann, Ishikawa, Noor and SP Iterations for Continuous Functions on an Arbitrary Interval, J. Comput. Appl. Math, 235(9): 3006-3014.
Picard E, 1890. Mémoire Sur la Théorie des Equations aux Dérivées Partielles et la Méthode des Approximations Successives, J. Math. Pure. Appl., 6: 145-210.
Sahu D.R, 2011. Applications of S iteration Process to Constrained Minimization Problems and Split Feasibility Problems, Fixed Point Theory, 12(1): 187-204.
Şahin A, Başarır M, 2016. Convergence and Data Dependence Results of An Iteration Process in A Hyperbolic Spaces, Filomat, 30(3): 569-582.
Şahin A, Kalkan Z, Arısoy H, 2017. On The Solution of A Nonlinear Volterra Integral Equation with Delay. Sakarya University Journal of Science, 21(6): 1367-1376.
Şoltuz S.M, Grosan T, 2008. Data Dependence for Ishikawa Iteration when Dealing with Contractive Like Operators. Fixed Point Theory and Applications, 2008(1): 1-7.
Weng X, 1991. Fixed Point Iteration for Local Strictly Pseudo-Contractive Mapping. Proceedings of the American Mathematical Society, 113(3): 727-731.