GRAPH CONVERGENCE AND GENERALIZED CAYLEY OPERATOR WITH AN APPLICATION TO A SYSTEM OF CAYLEY INCLUSIONS IN SEMI-INNER PRODUCT SPACES

Authors

  • 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

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 so- lution and discuss the convergence of iterative sequences generated by the perturbed iterative algorithm.

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Published

2023-02-20

Issue

Volume 28, Number 1, March 2023

Section

Articles