Fixed Point Theorems for Modified (alpha-psi-varphi-theta)-Rational Contractive Mappings in alpha-Complete b-Metric Spaces

Anchalee Kaewcharoen, Preeyaluk Chuadchawna

Abstract


In this paper, we introduce the notion of  modified (alpha-psi-varphi-theta)-rational contraction mappings  where some conditions of Bianchini-Grandolfi gauge function  varphi is omitted.  We establish the existence of the unique fixed point theorems for such mappings which are triangular $\alpha$-orbital admissible in alpha complete b-metric spaces. Moreover, we also prove the unique common fixed point theorem for  mappings $T$ and $g$ where T is a  modified (alpha-psi-varphi-theta)-rational contraction mapping with respect to g. Our results extend the fixed point theorems in alpha-complete metric spaces proved by Hussian et al. [N. Hussain, M. A. Kutbi and P. Salimi, Fixed point theory in alpha-complete metric spaces with applications, Abstr. Appl. Anal., (2014) Article ID 280817] to alpha-complete b-metric spaces.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|