Constantin P. Niculescu

Convex functions and their applications : a contemporary approach

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some o ...

Explosive solutions of elliptic equations with absorption and nonlinear gradient term

AbstractLetf be a non-decreasing C1-function such that

A note on Ostrowski's inequality

f > 0 on (0,\infty ), f(0) = 0, \int_1^\infty {1/\sqrt {F(t)} dt< \infty }

AN EXTENSION OF THE HERMITE-HADAMARD INEQUALITY THROUGH SUBHARMONIC FUNCTIONS*

andF(t)/f2a(t)→ 0 ast → ∞, whereF(t)=∫0tf(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|a=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded.

Stirling's Formula and Its Extension for the Gamma Function

Abstract Fan’s minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is obtained.

An Extension of the Mazur‐Ulam Theorem

This paper deals with the problem of estimating the deviation of the values of a function from its mean value. We consider the following special cases: (i) the case of random variables (attached to arbitrary probability fields); (ii) the comparison is performed additively or multiplicatively; (iii) the mean value is attached to a multiplicative averaging process.

Large Solutions for Semilinear Parabolic Equations Involving Some Special Classes of Nonlinearities

The Schauder fixed point theorem is extended to the context of metric spaces with global nonpositive curvature. Some applications are included.

An Overview of Absolute Continuity and Its Applications

In this paper we obtain a Hermite-Hadamard type inequality for a class of subharmonic functions. Our proofs rely essentially on the properties of elliptic partial differential equations of second order. Our study extends some recent results from (1), (2) and (6).