Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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A RANDOM GENERALIZED NONLINEAR IMPLICIT VARIATIONAL-LIKE INCLUSION WITH RANDOM FUZZY MAPPINGS

  • Khan, F.A. (Department of Mathematics, University of Tabuk) ;
  • Aljohani, A.S. (Department of Mathematics, University of Tabuk) ;
  • Alshehri, M.G. (Department of Mathematics, University of Tabuk) ;
  • Ali, J. (Department of Mathematics, Aligarh Muslim University)
  • Received : 2021.01.17
  • Accepted : 2021.04.05
  • Published : 2021.12.15
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Abstract

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

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Acknowledgement

The authors would like to thank the anonymous referees for their comments that helped us to improve this paper. Third author is supported by the Deanship of Scientific Research Unit (Project Grant Number: S-1441-0089), University of Tabuk, KSA.

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