scholarly journals On approximation and interpolation of entire functions with index-pair $(p,q)$

1994 ◽  
Vol 38 ◽  
pp. 255-267 ◽  
Author(s):  
H. S. Kasana ◽  
D. Kumar
Keyword(s):  
Entire Functions ◽  
Index Pair

scholarly journals Existence theorem for proximate type of entire functions with index-pair (p, q)

1987 ◽  
Vol 35 (1) ◽  
pp. 35-42 ◽  
Author(s):  
H. S. Kasana
Keyword(s):  
Entire Function ◽  
Existence Theorem ◽  
Entire Functions ◽  
Index Pair ◽  
Interesting Generalization

R.S.L. Srivastava and O.P. Juneja (1967) proved an existence theorem for the proximate type T (r) of an entire function with classical growth. For an interesting generalization of this theorem for an entire function with index-pair (p,q), which is due essentially to H.S. Kasana and S.K. Vaish (1984), a remarkably simple (and markedly different) construction of T (r) is presented here. The main theorem established here applies to a much larger class of entire functions with index-pair (p,q) than that considered earlier.

scholarly journals Uniqueness on entire functions and their nth order exact differences with two shared values

2020 ◽  
Vol 18 (1) ◽  
pp. 211-215
Author(s):  
Shengjiang Chen ◽  
Aizhu Xu
Keyword(s):  
Entire Function ◽  
Entire Functions ◽  
Shared Values ◽  
Simple Method ◽  
Exact Difference ◽  
Hyper Order

Abstract Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference {\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then {\Delta }_{c}^{n}f(z)\equiv f(z) . Our result improves the related results of Zhang and Liao [Sci. China A, 2014] and Gao et al. [Anal. Math., 2019] by using a simple method.

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