Монотонлă функци

Figure 1. A monotonically increasing function.

Figure 2. A monotonically decreasing function

Figure 3. A function that is not monotonic

Монотонлă функци тесе çавнашкал функцие калаççĕ, хăшĕ е чакмасть, е ÿсмест.

Калăпăр, $f$ функци пур тесе шутлăпăр: $M\subset \mathbb {R} \to \mathbb {R} .$. Вара

• $f$ функци $M$ талккăшра ÿсекенни пулать, енчен те

$\forall x_{1},x_{2}\in M,\;x_{1}>x_{2}\Rightarrow f(x_{1})\geq f(x_{2})$.

• $f$ функци $M$ талккăшра пăркаланми ÿсекенни пулать, енчен те

$\forall x_{1},x_{2}\in M,\;x_{1}>x_{2}\Rightarrow f(x_{1})>f(x_{2})$.

• $f$ функци $M$ талккăшра чакаканни пулать, енчен те

$\forall x_{1},x_{2}\in M,\;x_{1}>x_{2}\Rightarrow f(x)\leq f(x_{2})$.

• $f$ функци $M$ талккăшра пăркаланми чакаканни пулать, енчен те

$\forall x_{1},x_{2}\in M,\;x_{1}>x_{2}\Rightarrow f(x_{1})<f(x_{2})$.

(Пăркаланми) ÿсекен е чакакан функцие (пăркаланми) монотонлă теççĕ.

Вуламалли

• Bartle, Robert G. (1976). The elements of real analysis (second ed.).
• Grätzer, George (1971). Lattice theory: first concepts and distributive lattices. ISBN 0-7167-0442-0.
• Pemberton, Malcolm; Rau, Nicholas (2001). Mathematics for economists: an introductory textbook. Manchester University Press. ISBN 0-7190-3341-1.
• Renardy, Michael & Rogers, Robert C. (2004). An introduction to partial differential equations. Texts in Applied Mathematics 13 (Second ed.). New York: Springer-Verlag. p. 356. ISBN 0-387-00444-0.
• Riesz, Frigyes & Béla Szőkefalvi-Nagy (1990). Functional Analysis. Courier Dover Publications. ISBN 978-0-486-66289-3.
• Russell, Stuart J.; Norvig, Peter (2010). Artificial Intelligence: A Modern Approach (3rd ed.). Upper Saddle River, New Jersey: *Prentice Hall. ISBN 978-0-13-604259-4.
• Simon, Carl P.; Blume, Lawrence (April 1994). Mathematics for Economists (first ed.). ISBN 978-0-393-95733-4. (Definition 9.31)

Каçăсем

• Convergence of a Monotonic Sequence by Anik Debnath and Thomas Roxlo (The Harker School), Wolfram Demonstrations Project.