Lipschitz Type Analogue of Strict Contractive Conditions and Common Fixed Points

Ravindra K. Bisht


In this paper, we obtain a common xed point theorem for a pair of self mappings satisfying a Lipschitz type analogue of strict contractive condition by using a relatively new notion of conditional reciprocal continuity wherein we never require conditions on the completeness of the space, noncompatibility or property (E.A.), continuity of any mapping and completeness (or closedness) of the range of any one of the involved mappings. Our results substantially improve the results of Pant [Discontinuity and fixed points, J. Math. Anal. Appl. 240(1999) 284--289], Pant and Pant [Common xed points under strict contractive conditions, J. Math. Anal. Appl. 248 (2000) 327--332], Imdad et al. [Coincidencefixed points in symmetric spaces under strict contractions, J. Math. Anal. Appl. 320 (2006) 352--360] and Jin-Xuan and Yang [Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Anal. 70 (2009) 184--193].

Full Text: PDF


  • 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|