It is well known that there are a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc.. Generally speaking, it has become an important topic how to generalize monotonicity. Recently, Leindler [5] defined a ne...

In this paper, we introduce general classes of generalized monotonicity and generalized convexity. For each type of (relatively) generalized monotone map, we establish a relationship to (relatively) generalized convex function. In this way, we obtain first-order characterizations for various (relatively) generalized convex functions. Our results extend/generalize similar result obtained in [3].

The relaxation of the property monotonicity is a trend in theory aggregation and fusion functions several generalized forms have been introduced, most which are based on notion directional monotonicity. In this paper, we propose general framework for that encompasses different can find literature. Additionally, introduce various new not Specifically, dilative monotonicity, requires function inc...

In this paper, we introduce the notion of extended relaxed -monotonicity. We obtain existence solution of the generalized mixed equilibrium problems in reflexive Banach spaces with extended relaxed -monotonicity by using the KKM technique. Our results extend and improve the corresponding results in the existing literature.

A parametrized version of the nonlinear complementarity problem is formulated. The existence of a continuation of a solution is investigated and sufficient and necessary conditions for the monotonicity of such a continuation are given. The notions of strong and uniform monotonicity, originated in the linear theory, are discussed, and the theorems of the linear theory are generalized.

In the paper, three basic properties of the logarithmically N alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are obtained in [W. E. Clark and M. E. H. Ismail, Inequalities involving gamma and psi functions, Anal. Appl. (Singap.) 1 (2003), no. 1, 129–140.], are generalized to the logarithmically N -a...