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Unifying Some Implicit Common Fixed Point Theorems for Hybrid Pairs of Mappings in G-Metric Spaces through Altering Distance Function |
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PP: 1787-1798 |
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doi:10.18576/amis/100520
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Author(s) |
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Deepak Singh,
Vishal Joshi,
Jong Kyu Kim,
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Abstract |
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| In this paper, the notion of sub-compatibility for hybrid pair of mappings in the framework of G-metric spaces, is introduced.
The role of an appropriate implicit function concerning altering distance function is also highlighted which envelops a host of
contraction conditions, in one go. Employing this implicit relation some common fixed point theorems are proved for two hybrid pairs
of single and multivalued mappings in the structure of G-metric spaces. While proving our results, we utilize the idea of compatibility
for hybrid mappings due to Kneko et al. [1] together with subsequentially continuity due to Bouhadjera et al. [2] (also alternately
reciprocal continuity due to Singh et al. [3] together with sub-compatibility) as patterned in Imdad et al. [4]. In view of remarks given
in E. Karapinar et al. [5], our fixed point results can not be reduced to the results which are observed in Jleli et al. [6], in the setting
of hybrid pairs of mappings. This leads that our results are not the consequences of any fixed point results on metric spaces from the
existing literature. Some illustrative examples associated with their pictorial justifications are also presented which substantiate the
genuineness of the hypotheses and the degree of utility of our results. |
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