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Computation of solution of integral equations via fixed point results

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.
Wydawca
Rocznik
Strony
772--785
Opis fizyczny
Bibliogr. 36 poz., rys., tab., wykr.
Twórcy
  • Department of Mathematical Sciences, Faculty of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
  • Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India
autor
  • Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India
  • CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Bibliografia
  • [1] A. Sahin, Z. Kalkan, and H. Arisoy, On the solution of a nonlinear Volterra integral equation with delay, Sakarya Univ. J. Sci. 21 (2017), no. 6, 1367–13676.
  • [2] S. A. Khuri and A. Sayfy, An iterative method for boundary value problems, Nonlinear Sci. Lett. A 8 (2017), no. 2, 178–186.
  • [3] S. A. Khuri and A. Sayfy, Numerical solution of functional differential equations: a Green’s function based iterative approach, Int. J. Comput. Math. 95 (2018), no. 10, 1937–1949.
  • [4] Y. Mudasir, D. Singh, and A. Goyal, A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable, J. Fixed Point Theory Appl. 21 (2019), no. 1, Article number 33.
  • [5] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications, Fundam. Math. 3 (1922), 133–181.
  • [6] F. P. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044.
  • [7] D. Göhde, Zum Prinzip der kontraktiven abbildung, Math Nachr. 30 (1965), 251–258.
  • [8] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006.
  • [9] A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc. 132 (2004), 1435–1443.
  • [10] J. J. Nieto and R. Rodriguez-Löpez, Contractive mapping theorems in partially ordered sets and application to ordinary differential equations, Order. 22 (2005), 223–239.
  • [11] M. Bachar and M. A. Khamsi, On common approximate fixed points of monotone nonexpansive semigroups in Banach spaces, Fixed Point Theory Appl. 2015 (2015), Article ID 160.
  • [12] B. Abdullatif, B. Dehaish, and M. A. Khamsi, Browder and Göhde fixed point theorem for monotone nonexpansive mappings, Fixed Point Theory Appl. 2016 (2016), Article ID 20.
  • [13] Y. Song, P. Kumam, and Y. J. Cho, Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces, Fixed Point Theory Appl. 2016 (2016), Article ID 73.
  • [14] B. A. B. Dehaish, M. A. Khamsi, Mann iteration process for monotone nonexpansive mappings, Fixed Point Theory Appl, (2015), Article ID 177.
  • [15] I. Uddin, C. Garodia, and J. J. Nieto, Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equation, J Inequalities Appl. 2018 (2018), Article ID 339.
  • [16] W. R. Mann, Mean value methods in iteration, Proc. Am. Math. Soc. 4 (1953), 506–510.
  • [17] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147–150.
  • [18] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73 (1967), 957–961.
  • [19] M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), no. 1, 217–229.
  • [20] C. Garodia and I. Uddin, A new fixed point algorithm for finding the solution of a delay differential equation, Aims Math. 5 (2020), no. 4, 3182–3200.
  • [21] C. Garodia and I. Uddin, A new iterative method for solving split feasibility problem, J. Appl. Anal. Comput. 10 (2020), no. 3, 986–1004.
  • [22] C. Garodia, I. Uddin, and S. H. Khan, Approximating common fixed points by a new faster iteration process, Filomat 34 (2020), no. 6, 2047–2060.
  • [23] C. Garodia, I. Uddin, and D Baleanu, On constrained minimization, variational inequality and split feasibility problem via new iteration scheme in Banach spaces, Bulletin Iranian Math. Soc. 48 (2022), no. 4, 1493–1512.
  • [24] B. S. Thakur, D. Thakur, and M. Postolache, A new iteration scheme for approximating fixed points of nonexpansive mappings, Filomat. 30 (2016), no. 10, 2711–2720.
  • [25] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bulletin Australian Math. Soc. 43 (1991), 153–159.
  • [26] H. F. Senter and W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Am. Math. Soc. 44 (1974), no. 2, 375–380.
  • [27] A. Salim, S. Abbas, M. Benchohra, and E. Karapinar, Global stability results for Volterra-Hadamard random partial fractional integral equations, Rendiconti del Circolo MaT. di Palermo Series 2 (2022), 1–13.
  • [28] S. Abbas, M. Benchohra, J. Henderson, and J. E. Lazreg, Weak solutions for a coupled system of partial Pettis Hadamard fractional integral equations, Adv. Theory Nonlinear Anal. Appl. 1 (2017), no. 2, 136–146.
  • [29] I. A. Rus, Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle, Adv. Theory Nonlinear Anal. Appl. 3 (2019), no. 3, 111–120.
  • [30] S. K. Panda, E. Karapınar, and A. Atangana, A numerical schemes and comparisons for fixed point results with applications to the solutions of Volterra integral equations in dislocated extended b-metric space, Alexandria Eng. J. 59 (2020), no. 2, 815–827.
  • [31] B. Alqahtani, H. Aydi, E. Karapınar, and V. Rakocevic, A solution for Volterra fractional integral equations by hybrid contractions, Mathematics 7 (2019), no. 8, 694.
  • [32] H. Aydi, E. Karapinar, and H. Yazidi, Modified F-Contractions via alpha-admissible mappings and application to integral equations, Filomat. 31 (2017), no. 5, 1141–1148.
  • [33] E. Karapinar, A. Fulga, N. Shahzad, and A. F. Roldán López de Hierro, Solving integral equations by means of fixed point theory, J. Function Spaces 2022 (2022), 1–16, Article ID 7667499. doi: 10.1155/2022/7667499.
  • [34] L. Wangwe and S. Kumar, Fixed point theorems for multi-valued α F− -contractions in Partial metric spaces with an application, Results in Nonlinear Anal. 4 (2021), no. 3, 130–148.
  • [35] E. Karapınar, A. Atangana, and A. Fulga, Pata type contractions involving rational expressions with an application to integral equations, Discrete Continuous Dynam. Syst.-S. 14 (2021), no. 10, 3629.
  • [36] R. P. Agarwal, Ü. Aksoy, E. Karapınar, and İ.M. Erhan, F-contraction mappings on metric-like spaces in connection with integral equations on time scales, RACSAM. 114 (2020), no. 3, 1–12.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cfb80845-3b6f-43b5-84dd-1285f4cf7a4f
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