Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions

Abstract

The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique fixed point for this class of operators. Thirdly, we study Ulam-Hyers stability, well-posedness, and periodic point properties. Finally, an application of the main results to the variational inequality problem is given.

Keywords

• Kannan contraction
• interpolative Kannan type contraction
• enriched Kannan operators
• enriched interpolative Kannan type contraction
• fixed point
• well-posedness