On omitted value for transcendental semigroups

Subham Chatterjee (), Soumyadip Majee () and Gorachand Chakraborty ()
Additional contact information
Subham Chatterjee: Sidho-Kanho-Birsha University
Soumyadip Majee: Sidho-Kanho-Birsha University
Gorachand Chakraborty: Sidho-Kanho-Birsha University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 684-690

Abstract: Abstract In this paper, we define omitted value for transcendental semigroups and show that in a transcendental semigroup there can be at most one omitted value. Several examples of transcendental semigroups having omitted value are given. We define Baker wandering domain for transcendental semigroups. For a transcendental semigroup having a Baker wandering domain W as well as an omitted value a, we prove that a lies in the Julia set. We show that if two transcendental semigroups G and $$G^{\prime }$$ G ′ are conjugate under a map $$\psi $$ ψ and G has omitted value $$z_0$$ z 0 then $$G^{\prime }$$ G ′ has omitted value $$\psi (z_0)$$ ψ ( z 0 ) . We show that if $$G=\; $$ G = such that g is conjugate of f under the map $$\psi $$ ψ and f has omitted value $$z_0$$ z 0 then $$O(G)=\{z_0\}$$ O ( G ) = { z 0 } if and only if $$\psi (z_0)\,=\,z_0$$ ψ ( z 0 ) = z 0 . Finally, we conclude this paper by giving some problems for future research.

Keywords: Entire function; Omitted value; Transcendental semigroup; Conjugate semigroup; Baker wandering domain; 37F44; 37F10; 30D05 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-023-00396-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:55:y:2024:i:2:d:10.1007_s13226-023-00396-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-023-00396-0

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().