## Taiwanese Journal of Mathematics

### $\left( \Phi ,\rho \right)$-MONOTONICITY AND GENERALIZED $\left(\Phi ,\rho \right)$-MONOTONICITY

#### Abstract

In this paper, new concepts of monotonicity, namely $\left( \Phi, \rho \right)$-monotonicity, $\left( \Phi, \rho \right)$-pseudo-monotonicity and $\left( \Phi, \rho \right)$-quasi-monotonicity are introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate $\left( \Phi, \rho \right)$-invexity and generalized $\left( \Phi, \rho \right)$-invexity of the function with $\left( \Phi, \rho \right)$-monotonicity and generalized $\left( \Phi, \rho \right)$-monotonicity of its gradient.

#### Article information

Source
Taiwanese J. Math., Volume 18, Number 1 (2014), 237-255.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706340

Digital Object Identifier
doi:10.11650/tjm.18.2014.3048

Mathematical Reviews number (MathSciNet)
MR3162122

Zentralblatt MATH identifier
1357.47052

#### Citation

Antczak, Tadeusz. $\left( \Phi ,\rho \right)$-MONOTONICITY AND GENERALIZED $\left(\Phi ,\rho \right)$-MONOTONICITY. Taiwanese J. Math. 18 (2014), no. 1, 237--255. doi:10.11650/tjm.18.2014.3048. https://projecteuclid.org/euclid.twjm/1499706340

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