Limit summability of ultra exponential functions

Document Type: Research Articles

Author

دانشگاه آزاد واحد شیراز

Abstract

In [1] we uniquely introduced ultra exponential functions (uxpa) and de ned
next step of the serial binary operations: addition, multiplication and power.
Also, we exhibited the topic of limit summability of real functions in [2,3]. In
this paper, we study limit summability of the ultra exponential functions and
prove some of their properties. Finally, we pose an unsolved problem about
them.

[1] M.H. Hooshmand, Ultra Power and Ultra Exponential Functions, Integral
Transforms Spec. Funct., Vol. 17, No. 8 (2006), 549-558.
[2] M.H. Hooshmand, Limit Summability of Real Functions, Real Analysis
Exchange, Volume 27 (2002), Number 2, Pages 463-472.
[3] M.H. Hooshmand, Another Look at the Limit Summability of Real
Functions, J. of Math. Extension, Vol. 4, No. 1 , Ser. No. 7 (2009), 73-89.
[4] R. J. Webster, Log-Convex Solutions to the Functional Equation f(x+1) =
g(x)f(x): 􀀀 -Type Functions, J. Math. Anal. Appl., 209 (1997), 605-623.