Relaxed resolvent operator for solving a variational inclusion problem

Iqbal Ahmad, Mijanur Rahaman, Rais Ahmad

Abstract


In this paper, we introduce a new resolvent operator and we call it relaxed resolvent operator. We prove that relaxed resolvent operator is single-valued and Lipschitz continuous and finally we appropriate the solution of a variational inclusion problem in Hilbert spaces by defining an iterative algorithm based on relaxed resolvent operator. A few concepts like Lipschitz continuity and strong monotonicity are used to prove the main result of this paper. Thus, no strong conditions are used. Some examples are constructed.

Keywords


Relaxed; Inclusion; Space; Algorithm; Lipschitz.

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DOI: 10.19139/soic.v4i2.166

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