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)


DOI: https://doi.org/10.58250/jnanabha.2020.50105

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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