Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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GRAPH CONVERGENCE AND GENERALIZED CAYLEY OPERATOR WITH AN APPLICATION TO A SYSTEM OF CAYLEY INCLUSIONS IN SEMI-INNER PRODUCT SPACES

  • Mudasir A. Malik (Department of Mathematics, University of Kashmir South Campus) ;
  • Mohd Iqbal Bhat (Department of Mathematics, University of Kashmir South Campus) ;
  • Ho Geun Hyun (Department of Mathematics Education, Kyungnam University)
  • Received : 2022.06.04
  • Accepted : 2022.09.30
  • Published : 2023.03.03
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Abstract

In this paper, we introduce and study a generalized Cayley operator associated to H(·, ·)-monotone operator in semi-inner product spaces. Using the notion of graph convergence, we give the equivalence result between graph convergence and convergence of generalized Cayley operator for the H(·, ·)-monotone operator without using the convergence of the associated resolvent operator. To support our claim, we construct a numerical example. As an application, we consider a system of generalized Cayley inclusions involving H(·, ·)-monotone operators and give the existence and uniqueness of the solution for this system. Finally, we propose a perturbed iterative algorithm for finding the approximate solution and discuss the convergence of iterative sequences generated by the perturbed iterative algorithm.

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References

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