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Demonstratio Mathematica

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Volume 47, Issue 4


Hybrid Fixed Point Theorems in Symmetric Spaces via Common Limit Range Property

Mohammad Imdad / Sunny Chauhan / Ahmed H. Soliman / M. A. Ahmed
Published Online: 2014-12-11 | DOI: https://doi.org/10.2478/dema-2014-0075


In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012), 611-620) are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.

Keywords: and phrases symmetric space; multi-valued mappings; quasi-coincidentally commuting mappings; common limit range property; coincidence point; common fixed point


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About the article

Received: 2013-03-12

Published Online: 2014-12-11

Published in Print: 2014-12-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 4, Pages 949–962, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0075.

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© by Mohammad Imdad. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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