Fixed point results of enriched interpolative Kannan type operators with applications

• Abbas, Mujahid ^[1] ; Anjum, Rizwan ^[2] ; Riasat, Shakeela ^[3]
  1. [1] University of Pretoria

     University of Pretoria

     City of Tshwane, Sudáfrica

     
  2. [2] Riphah International University

     Riphah International University

     Pakistán

     
  3. [3] Government College University

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 391-404
• Idioma: inglés
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• Resumen

  • The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains theclasses of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskij iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problems is solved.