Jñānābha‎, Vol. 50 (1) (2020), 43-48

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.