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On pointwise convergence of the family of Urysohn‐type integral operators
Author(s) -
Almali Sevgi Esen
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5376
Subject(s) - mathematics , pointwise convergence , pointwise , type (biology) , bounded function , kernel (algebra) , function (biology) , convergence (economics) , pure mathematics , infinity , mathematical analysis , nonlinear system , monotonic function , ecology , approx , physics , quantum mechanics , evolutionary biology , computer science , economics , biology , economic growth , operating system
In this paper, we consider a family of nonlinear integral operators of Urysohn‐type and study the pointwise convergence of the family at characteristic points of L 1 −function. The kernel K λ ( x , t , u ( t )) depends on the positive parameter λ changing on the set of numbers with the accumulation point at infinity and K λ ( x , t , u ( t )) is an entire analytic function of variable u , which is a bounded function belonging to L 1 ( R ).