International Journal of Nonlinear Analysis and Applications

A split common fixed point and null point problem for Lipschitzian $J-$quasi pseudocontractive mappings in Banach spaces

Document Type : Research Paper

Authors

Department of Mathematics, University of Uyo, P. M. B. 1017, Uyo, Nigeria

Abstract

A split common fixed point and null point problem (SCFPNPP) which includes the split common fixed point problem, the split common null point problem and other problems related to the fixed point problem and the null point problem is studied. We introduce a Halpern--Ishikawa type algorithm for studying the split common fixed point and null point problem for Lipschitzian $J-$quasi pseudocontractive operators and maximal monotone operators in real Banach spaces. Moreover, we establish a strong convergence results under some suitable conditions and reduce our main result to the above-mentioned problems. Finally, we applied the study to split feasibility problem (FEP), split equilibrium problem (SEP), split variational inequality problem (SVIP) and split optimization problem (SOP).

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 1827-1853
  • Receive Date: 04 February 2021
  • Revise Date: 09 May 2021
  • Accept Date: 25 May 2021