We prove uniform convexity of solutions to the capillarity boundary value problem for fixed boundary angle in (0, π/2) and strictly positive capillarity constant provided that the base domain Ω ⊂ R is sufficiently close to a disk in a suitable C-sense.

The main objective of this paper is to establish some sufficient conditions so that a class normalized Mittag–Leffler-type functions satisfies several geometric properties such as starlikeness, convexity, close-to-convexity, and uniform convexity inside the unit disk. Moreover, pre-starlikeness k-uniform are discussed for these functions. Some also derived belong Hardy spaces Hp H∞. Furthermore...

Those kinds of infinite direct sums are characterized for which NUC (NUS, respectively) is inherited from the component spaces to the direct sum. 1. NUC and the lower KK-modulus. The Banach space X is said to be nearly uniformly convex, abbreviated NUC (cf. [2]), if: for every ε > 0, there exists δ > 0 such that the convex hull conv{xn} of every sequence {xn} in the unit ball BX of X with separ...

In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in infinite dimensional settings and use the connections in order to obtain improved convergence results concerning...

Abstract This paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property spaces which similar nearly convexity Banach setting. Using property, several new theorems nonexpansive

In this paper, four parameters Wright function is considered. Certain geometric properties such as starlikeness, convexity, uniform convexity and close-to-convexity are discussed for function. Further, certain of normalized Bessel the first kind two studied a consequence. Interesting corollaries examples provided to support that these results better than existing ones improve several available ...