In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.

We define a family {γ(P)} of generalized Euler constants indexed by finite sets of primes P and study their distribution. An apparent monotonicity is investigated.

In this paper, We introduce a new class of generalized vector complementarity problems and the corresponding generalized vector variational inequality problems which include many known complementarity problems and the corresponding vector variational inequality problems as special cases and establish the equivalence between those problems in Banach spaces. Furthermore, we obtain some new existe...

Abstract In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is...

New concepts of generalized ρ, θ -η invex functions for non-differentiable functions and generalized ρ, θ -η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized ρ, θ -η invexity of functions and generalized ρ, θ -η invariant monotonicity of the corresponding Clarke’s subdifferentials are studied. Some of our results are extension and improv...

In the preprint [1] one of the authors formulated some conjectures on monotonicity of ratios for exponential series sections. They lead to more general conjecture on monotonicity of ratios of Kummer hypergeometric functions and was not proved from 1993. In this paper we prove some conjectures from [1] for Kummer hypergeometric functions and its further generalizations for Gauss and generalized ...