Abstract
In this paper, in the light of weighted sharing of sets, we investigate the possible uniqueness of meromorphic function of restricted hyper order with its linear c-shift operator. Our first two theorems improve a number of earlier results. Our last theorem together with a corollary improves and extends a result due to Li, Lu and Xu [14]. Most importantly, our another corollary deducted from the last theorem not only provides an answer to an open question posed by Liu [16] but also noticeably improves two results of Chen and Chen [4]. A number of examples have been exhibited by us pertinent with the content of the paper. At the penultimate section which is also the application part of our result, we extend a recent result of Liu, Ma and Zhai [17]. Finally, presenting two examples, we conjecture that one of our result may hold for a larger class of functions and we place it as an open question for future investigations.
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The authors wish to thank the referees for their valuable suggestions and comments towards the improvement of the paper.
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The first author is thankful to DST PURSE programme for financial assistance.
The second author is thankful to the Council of Scientific and Industrial Research (India) for their financial support under File No 09/106 (0188)/2019-EMR-I.
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Banerjee, A., Roy, A. Meromorphic functions of restricted hyper-order sharing one or two sets with its linear C-shift operator. Anal Math 47, 747–779 (2021). https://doi.org/10.1007/s10476-021-0106-6
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DOI: https://doi.org/10.1007/s10476-021-0106-6