Nonlinear Functional Analysis and Applications

  • 제26권5호
  • /
  • Pages.869-885
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  • 2021
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  • 1229-1595(pISSN)
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  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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APPROXIMATION OF FIXED POINTS AND THE SOLUTION OF A NONLINEAR INTEGRAL EQUATION

  • Ali, Faeem (Department of Mathematics, Aligarh Muslim University) ;
  • Ali, Javid (Department of Mathematics, Aligarh Muslim University) ;
  • Rodriguez-Lopez, Rosana (Department of Statistics, Mathematical Analysis and Optimization Faculty of Mathematics, University of Santiago de Compostela)
  • 투고 : 2020.09.18
  • 심사 : 2021.04.12
  • 발행 : 2021.12.15
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초록

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

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참고문헌

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