Convergence analysis of a resolvent-free method for solving inclusion problems beyond Co-coercivity

Abstract In this paper, we introduce a new self-adaptive Tseng-type method for solving inclusion problems. Our method by-passes the co-coercivity condition and does not require any computation of the resolvent (or metric projection) operator. While incorporating the golden ratio technique, we prove weak, strong and $$R-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> Linear convergence of our method, and apply our result to solving the critical point problems. Furthermore, we conduct computational experiments to illustrate the performance of our iterative scheme over similar methods in literature.