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1

Reiterated periodic homogenization of integral functionals with convex and nonstandard growth integrands

Tachago Joel Fotso, Nnang Hubert, Zappale Elvira

Opuscula Mathematica

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2021

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Vol. 41, no. 1

113--143

EN

Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems involving convex functionals, converges to the minimizers of a homogenized problem with a suitable convex function.

2

Optimal bounds for the sine and hyperbolic tangent means II

Nowicka Monika, Witkowski Alfred

Journal of Applied Analysis

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2021

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Vol. 27, nr 1

65--72

EN

We provide the optimal bounds for the sine and hyperbolic tangent means in terms of various weighted means of the arithmetic and the contraharmonic means.

3

Length problems for Bazilevič functions

Nunokawa Mamoru, Sokół Janusz, Tang Huo

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

56--60

EN

Let C(r) denote the curve which is image of the circle |z|=r<1 under the mapping f. Let L(r) be the length of C(r) and A(r) the area enclosed by the curve C(r). Furthermore M(r) = max|z|=r |f(z)|. We present some relations between these notions for Bazilevič functions.

4

An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers

Sokół J., İlhan S., Güney H. Ö.

Journal of Mathematics and Applications

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2018

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Vol. 41

195--206

EN

We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions.

5

Fekete-Szegö problems for certain class of analytic functions associated with quasi-subordination

Sahoo P.

Journal of Mathematics and Applications

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2017

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Vol. 40

161--170

EN

In this paper, we determine the coefficient estimates and the Fekete-Szegö inequalities for [wzór], the class of analytic and univalent functions associated with quasi-subordination.

6

Some new fractional Fejér type inequalities for convex functions

Set E., Mumcu Î.

Fasciculi Mathematici

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2017

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Nr 59

145--157

EN

In this paper, firstly, a new identity for conformable fractional integrals is established. Then by making use of the established identity, some new fractional Fejér type inequalities are established. The results presented here have some relationships with the results of Set et al. (2015), proved in [6].

7

On Korenblum convex functions

Ereú J., López L., Merentes N.

Commentationes Mathematicae

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2017

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Vol 57, No. 1

25--44

EN

We introduce a new class of generalized convex functions called the K-convex functions, based on Korenblum’s concept of k-decreasing functions, where K is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second k-variation, extending a result of F. Riesz. We also present a formal structural decomposition result for the K-convex functions.

8

More on Ostrowski type inequalities for some s-convex functions in the second sense

Liu Z.

Demonstratio Mathematica

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2016

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Vol. 49, nr 4

398--412

EN

Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.

9

Conditionally approximately convex functions

Najdecki A., Tabor J.

Demonstratio Mathematica

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2016

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Vol. 49, nr 1

11--17

EN

Let X be a real normed space, V be a subset of X and α: [0, ∞) → [0, ∞) be a nondecreasing function. We say that a function f : V → [-∞, ∞) is conditionally α-convex if for each convex combination (…) of elements from V such that (…), the following inequality holds true (…). We present some necessary and some sufficient conditions for f to be conditionally α-convex.

10

A new characterizationof convex Φ-functions with a parameter

Micherda B.

Opuscula Mathematica

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2015

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Vol. 35, no. 2

191--197

EN

We show that, under some additional assumptions, all projection operators onto latticially closed subsets of the Orlicz-Musielak space generated by Φ are isotonic if and only if Φ is convex with respect to its second variable. A dual result of this type is also proven for antiprojections. This gives the positive answer to the problem presented in Opuscula Mathematica in 2012.

11

Conjugate functions, lp-norm like functionals, the generalized Hölder inequality, Minkowski inequality and subhomogeneity

Matkowski J.

Opuscula Mathematica

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2014

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Vol. 34, no. 3

523-560

EN

For h : (0,∞) → R, the function h* (t) := th( 1/t ) is called (*)-conjugate to h. This conjugacy is related to the Hölder and Minkowski inequalities. Several properties of (*)-conjugacy are proved. If φ and φ* are bijections of (0,∞) then [formula]. Under some natural rate of growth conditions at 0 and ∞, if φ is increasing, convex, geometrically convex, then [formula] has the same properties. We show that the Young conjugate functions do not have this property. For a measure space (Ω,Σ,μ) denote by S = (Ω,Σ,μ) the space of all μ-integrable simple functions x : Ω → R, Given a bijection φ : (0,∞) → (0,∞) define [formula] by [formula] where Ω(x) is the support of x. Applying some properties of the (*) operation, we prove that if ƒ xy ≤ Pφ(x)Pψ (y) where [formula] and [formula] are conjugate, then φ and ψ are conjugate power functions. The existence of nonpower bijections φ and ψ with conjugate inverse functions [formula] such that Pφ and Pψ are subadditive and subhomogeneous is considered.

12

Some Ostrowski’s type inequalities for functions whose second derivatives are s-convex in the second sense

Set E., Sarikaya M. Z., Ozdemir M. E.

Demonstratio Mathematica

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2014

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Vol. 47, nr 1

37--47

EN

Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.

13

Convolution properties of subclasses of analytic functions associated with the Dziok-Srivastava operator

Goyal S. P., Bansal S. K., Goswami P., Wang Z.-G.

Journal of Mathematics and Applications

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2013

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Vol. 36

71--77

EN

The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok-Srivastava operator. We further investigate convolution properties for these calsses. We also nd necessary and sufficient condition and coefficient estimate for them.

14

Applications of convolution properties

Trojnar-Spelina L.

Demonstratio Mathematica

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2013

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Vol. 46, nr 3

513--523

EN

K. I. Noor (2007 Appl. Math. Comput. 188, 814–823) has defined the classes Qk(a, b, λ, γ) and Tk(a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes.

15

A class of univalent functions involving a differentio-integral operator

Jain P. K., Sharma P., Jain V.

Demonstratio Mathematica

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2013

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Vol. 46, nr 2

283--297

EN

This paper focuses on a generalized linear operator Im which is a combination of both differential and integral operators. Involving this operator, a class Tsk(...) with respect to k-symmetric points is defined. Results based on coefficient inequalities and bounds for this class are obtained. Various integral representations and some consequent results for TS(...) class are also determined. Further, results on partial sums are discussed.

16

On some inequality of Hermite-Hadamard type

Wąsowicz S., Witkowski A.

Opuscula Mathematica

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2012

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Vol. 32, no. 3

591-600

EN

It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality comparing the methods of the approximate integration, which is optimal. We also present its counterpart of Fejér type.

17

Close-to-convexity properties of basic hypergeometric functions using their Taylor coefficients

Raghavendar K., Swaminathan A.

Journal of Mathematics and Applications

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2012

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Vol. 35

53--67

EN

In this paper, we find the conditions on parameters a, b, c and q such that the basic hypergeometric function zφ(a,b;c;q,z) and its q-Alexander transform are close-to-convex (and hence univalent) in the unit disc D:={z: |z|<1}.

18

Weak nearly uniform smoothness of the ψ-direct sums (X1 O…O XN)ψ

Kato M., Tamura T.

Commentationes Mathematicae

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2012

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Vol. 52, [Z] 2

171--198

EN

We shall characterize the weak nearly uniform smoothness of the ψ-direct sum (X1 O…O XN)ψof N Banach spaces X1,..., XN, where ψ is a convex function satisfying certain conditions on the convex set [formula]. To do this, a class of convex functions which yield l1-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular, an example which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square will be presented.

19

Subclasses of univalent functions related with circular domains

Trojnar-Spelina L.

Journal of Mathematics and Applications

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2011

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Vol. 34

109--116

EN

We investigate the family of functions normalized by the condition ƒ(0) = ƒ(0) - 1 = 0, that are analytic in the unit disk, with the property that the domain of values [...] is the disk |z-b| < b, b ≥ 1. Integral and convolution characterizations are found and coefficients bounds are given.

20

Inclusion relationship and Fekete-Szegö like inequalities for a subclass of meromorphic functions

Răducanu D., Orhan H., Deniz E.

Journal of Mathematics and Applications

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2011

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Vol. 34

87--95

EN

In this paper using a differential operator, we define a new subclass of meromorphic functions. Sharp upper bounds for the functional […] in this class are obtained. An inclusion property is also given.