CARISTI-BANACH TYPE CONTRACTION VIA SIMULATION FUNCTION By Swati Antal and U. C. Gairola Department of Mathematics H. N. B. Garhwal University, BGR Campus Pauri Garhwal-246001, Uttarakhand, India. Email:antalswati11@gmail.com, ucgairola@rediffmail.com (Received : February 09, 2020 ; Revised: February 22, 2020) Abstract In this paper we introduce the notion of a Caristi-Banach type ZbR - contraction in the framework of b-metric space endowed with a transitive relation that combine the ideas of Caristi type contraction and Banach contraction with a help of simulation function. We present an example to clarify the statement of the given result. 2010 Mathematics Subject Classifications: 47H10, 54H25. Keywords and phrases: Caristi-Banach type ZbR - contraction, Simulation function, transitive relation. |
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