Entire functions of restricted hyper-order sharing a set of two small functions IM with their linear c-shift operators

Abstract

Purpose – The paper aims to build the relationship between an entire function of restricted hyper-order with its linear c-shift operator. Design/methodology/approach – Standard methodology for papers in difference and shift operators and value distribution theory have been used. Findings – The relation between an entire function of restricted hyper-order with its linear c-shift operator was found under the periphery of sharing a set of two small functions IM (ignoring multiplicities) when exponent of convergence of zeros is strictly less than its order. This research work is an improvement and extension of two previous papers. Originality/value – This is an original research work.

Keywords

• Entire functions
• Exponent of convergence
• Hyper-order
• Linear c-shift operator
• Shared set