Funksional tenglama

Matematikada funksional tenglama — nomaʼlumi funksiya boʻlib keladigan har qanday tenglama. Koʻpincha, tenglama funksiyaning (yoki funksiyalarning) bir nuqtadagi qiymatini boshqa nuqtalardagi qiymatlari bilan bogʻlaydi. Masalan, funksiyalarning qiymatlarini ular qanoatlantiradigan funksional tenglamalarning turlarini koʻrib chiqish orqali aniqlash mumkin. Funksional tenglama atamasi odatda algebraik tenglamalar yoki differensial tenglamalarga keltirish mumkin boʻlmagan tenglamalarni anglatadi.

Misol

$f(s)=2^{s}\pi ^{s-1}\sin \left({\frac {\pi s}{2}}\right)\Gamma (1-s)f(1-s)$

koʻrinishidagi tenglamani Riemann zeta funksiyasi qanoatlantiradi. Bu yerdagi Γ harfi gamma-funksiyani anglatadi.

Manbalar

• János Aczél, Lectures on Functional Equations and Their Applications, Academic Press, 1966, reprinted by Dover Publications, ISBN 0486445232 .
• János Aczél & J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989.
• C. Efthimiou, Introduction to Functional Equations, AMS, 2011, ISBN 978-0-8218-5314-6 ; online (Wayback Machine saytida 2020-11-25 sanasida arxivlangan).
• Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, 2009.
• Marek Kuczma, Introduction to the Theory of Functional Equations and Inequalities, second edition, Birkhäuser, 2009.
• Henrik Stetkær, Functional Equations on Groups, first edition, World Scientific Publishing, 2013.
• Christopher G. Small. Functional Equations and How to Solve Them. Springer Science & Business Media, 3-aprel 2007. ISBN 978-0-387-48901-8. 

Havolalar

• Funksional tenglamalar va ularning yechilish usullari EqWorld saytida