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In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, by considering the identity established by Luo et al. in [C. Luo, T.-S. Du, M. Kunt and Y. Zhang, Certain new bounds considering the weighted Simpson-like type inequality and applications, J. Inequal. Appl. 2018 2018, Paper No. 332] and under the assumption of the quasi-convexity of the first derivative, we establish some new error estimates of the Simpson-like type inequalities. We also discuss the case where the first derivative satisfies the Hölder condition. At the end, we provide some applications to special means. The obtained results represent a continuation of the above-mentioned paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find coefficient estimates for the class of functions ℳ N (γ , ϑ , λ) consisting of analytic functions f normalized by f(0) = f′(0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a2, a3, and the Fekete-Szegő functional upper bound for f ∈ ℳ N (γ , ϑ , λ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the singular k-Hessian equations S k ⁢ (λ ⁢ (D 2 ⁢ u)) = h ⁢ (x) ⁢ f ⁢ (- u) + g ⁢ (| D ⁢ u |) in ⁢ Ω and S k ⁢ (λ ⁢ (D 2 ⁢ u)) = h ⁢ (x) ⁢ f ⁢ (- u) ⁢ (1 + g ⁢ (| D ⁢ u |) ) in ⁢ Ω with the Dirichlet boundary condition u = 0 on ∂ ⁡ Ω , where Ω ⊂ ℝ N ( N ≥ 2 ) is a strictly convex, bounded smooth domain. Using the method of upper and lower solutions and the Karamata regular variation theory, we get new criteria of the existence and asymptotic behavior of strictly convex solutions under different conditions imposed on h, f and g. This problem is more difficult to solve than the k-Hessian problem without gradient terms, and requires additional new conditions in the proof process. [ABSTRACT FROM AUTHOR]

In this paper, we first define ray increasing and decreasing monotonicity of maps. If 푇 is an optimal transport map for the Monge problem with cost function ∥ y - x ∥ sc in R n or 푇 is an optimal transport map for the Monge problem with cost function d ⁢ (x , y) , the geodesic distance, in more general, non-branching geodesic spaces 푋, we show respectively equivalence of some previously introduced monotonicity properties and the property of ray increasing as well as ray decreasing monotonicity which we define in this paper. Then, by solving secondary variational problems associated with strictly convex and concave functions respectively, we show that there exist ray increasing and decreasing optimal transport maps for the Monge problem with cost function ∥ y - x ∥ sc . Finally, we give the classification of optimal transport maps for the Monge problem such that the cost function ∥ y - x ∥ sc further satisfies the uniform smoothness and convexity estimates. That is, all of the optimal transport maps for such Monge problem can be divided into three different classes: the ray increasing map, the ray decreasing map and others. [ABSTRACT FROM AUTHOR]

In this paper, we study the higher-order Schwarzian derivative Sn(f) proposed by H. Tamanoi [Higher Schwarzian operators and combinatorics of the Schwarzian derivative, Math. Ann. 305 (1996), 127–151]. For the strongly starlike functions of order α and strongly convex functions of order α, the sharp bound of |S3(f)(0)| is obtained. When n ∈ [2, 7], we prove that the higher Bers maps induced by Sn(f) on Weil-Petersson Teichmüller space and BMO-Teichmüller space are holomorphic. [ABSTRACT FROM AUTHOR]

In this paper, an equality is proved for twice differentiable convex functions involving Riemann–Liouville fractional integral. With the help of this equality, there are established several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann–Liouville fractional integral. [ABSTRACT FROM AUTHOR]

Content industries have several profit sources that positively interact with one another, and piracy affects them not only negatively but also positively. For copyright holders, choosing to allow piracy depends upon its total external effects. This paper proves that in such case the profit function is convex with respect to the level of enforcement. This paper shows a convex profit function with respect to the level of enforcement. The convexity leads to a corner solution of optimal enforcement for copyright holders. Which corner solution is selected depends on the relative size of the sub-market, and no enforcement is profitable if the submarket size is relatively large. This result compensates for a shortcoming of discussions that assume only two options regarding the level of enforcement, zero or perfect enforcement. [ABSTRACT FROM AUTHOR]

In [Logarithmic coefficient bounds and coefficient conjectures for classes associated with convex functions, J. Funct. Spaces 2021 (2021), Art. ID 6690027], Alimohammadi et al. presented a few conjectures for the logarithmic coefficients γn of the functions f belonging to some well-known classes like C (1 + α z) for α ∈ (0, 1], and C V h p l (1 / 2). For example, it is conjectured that if the function f ∈ C (1 + α z) , then the logarithmic coefficients of f satisfy the inequalities | γ n | ≤ α 2 n (n + 1) , n ∈ N. Equality is attained for the function Lα, n, that is, log L α , n (z) z = 2 ∑ n = 1 ∞ γ n (L α , n) z n = α n (n + 1) z n + ... , z ∈ U. The aim of this paper is to confirm that these conjectures hold for the coefficient γn0−1 whenever the function f has the form f (z) = z + ∑ k = n 0 ∞ a k z k , z ∈ U for some n 0 ∈ N , n0⩾2. [ABSTRACT FROM AUTHOR]

In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with Hankel determinants for starlike and convex functions related to modified sigmoid functions. Sharp bounds are given for second and third Hankel determinants. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some norm inequalities involving convex and concave functions, which are the generalizations of the classical Clarkson inequalities. Let A1, . . . , An be bounded linear operators on a complex separable Hilbert space H and let α1, . . ., αn be positive real numbers such that ∑j=1nαj = 1. We show that for every unitarily invariant norm, If ƒ is a non-negative function on [0, ∞) such that ƒ(0) = 0 and g(t) = ƒ(t) is convex, then |||∑j=1nαjƒ(|Aj|)||| ≥ |||∑j,k∈Sℓ (ƒ(√αjαk /4αℓ(1−αℓ)| Aj + Ak − 2 ∑j=1nαjAj|) + ƒ(√αjαk(2αℓ−1)/4αℓ(1−αℓ)| Aj − Ak|)) + ƒ(|∑j=1nαjAj|)||| for ℓ = 1, . . . , n. If ƒ is a non-negative function on [0, ∞) such that g(t) = ƒ(√t) is concave, then the inverse inequality holds. Here, the symbol Sℓ = {1, . . . , n} ∖ {ℓ} for ℓ ∈ {1, . . . , n}. In addition, we provide some applications of the above inequalities. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to determine the radii of starlikeness and convexity of the generalized k-Bessel functions for three different kinds of normalization in such a way that the resulting functions are analytic in the unit disk of the complex plane. The characterization of entire functions from Laguerre–Pólya class plays a significant role in this paper. Moreover, the interlacing properties of the zeros of the k-Bessel function and its derivative is also useful in the proof of the main results. By making use of the Euler–Rayleigh inequalities for the real zeros of the generalized k-Bessel function, we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of mild solutions for nonlocal fractional semilinear differential inclusions with noninstantaneous impulses of order α ∈ (1,2) and generated by a cosine family of bounded linear operators. Moreover, we show the compactness of the solution set. We consider both the case when the values of the multivalued function are convex and nonconvex. Examples are given to illustrate the theory. [ABSTRACT FROM AUTHOR]

For normalized starlike functions f : 픻 → ℂ, we consider the analytic functions g : 픻 → ℂ defined by g(z) = (1 + z(f″(z))/f′(z))/(zf′(z)/f(z)) and g(z) = (1 − α)(zf′(z))/f(z) + α(1 + (zf″(z))/f′(z)), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g(ρ z) is subordinate to various functions with positive real part. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Totally Relaxed Self-adaptive Subgradient Extragradient Method (TRSSEM) with Halpern iterative scheme for finding a common solution of a Variational Inequality Problem (VIP) and the fixed point of quasi-nonexpansive mapping in a 2-uniformly convex and uniformly smooth Banach space. The TRSSEM does not require the computation of projection onto the feasible set of the VIP; instead, it uses a projection onto a finite intersection of sub-level sets of convex functions. The advantage of this is that any general convex feasible set can be involved in the VIP. We also introduce a modified TRSSEM which involves the projection onto the set of a convex combination of some convex functions. Under some mild conditions, we prove a strong convergence theorem for our algorithm and also present an application of our theorem to the approximation of a solution of nonlinear integral equations of Hammerstein's type. Some numerical examples are presented to illustrate the performance of our method as well as comparing it with some related methods in the literature. Our algorithm is simple and easy to implement for computation. [ABSTRACT FROM AUTHOR]

We generalize cyclic Jensen's inequality utilizing the theory of 4-convex function under the effect of introduced Green functions. We formulate result for power means and quasi means. Also we give applications in information theory by giving new estimations of generalized Csiszár divergence, Rényi-divergence, Shannon-entropy, Kullback-Leibler divergence and χ2-divergence. [ABSTRACT FROM AUTHOR]

We investigate the non-univalent function's properties reminiscent of the theory of univalent starlike functions. Let the analytic function ψ (z) = ∑ i = 1 ∞ A i z i , A1 ≠ 0 be univalent in the unitdisk. Non-univalent functions may be found in the class ℱ (ψ) of analytic functions f of the form f (z) = z + ∑ k = 2 ∞ a k z k satisfying (zf′ (z)/f (z) – 1) ≺ ψ(z). Such functions, like the Ma and Minda classes k=2 of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class ℱ (ψ) . Non-analytic functions that share properties of analytic functions are known as poly-analytic functions. Moreover, we compute Bohr and Rogosinski's radius for poly-analytic functions with analytic counterparts in the class ℱ (ψ) or classes of Ma-Minda starlike and convex functions. [ABSTRACT FROM AUTHOR]

Natural phenomena as well as problems encountered in pure and applied sciences are modeled by ordinary, partial or integral differential equations. Most of these problems have a nonlinear aspect which makes their studies difficult, or even impossible. For this, they must resort to other alternatives; among the methods used is the integral inequalities approach, which allows the study of quantitative and qualitative properties of solutions such as existence, uniqueness, delimitation, oscillation, and stability. In this study, we present some new integral inequalities of the Gronwall–Bellman–Bihari type associated with the fractional derivative of ψ-Hilfer, which represents a strong tool and is applicable in the study of certain differential equations. Several known results are derived and some applications to ordinary differential equations are provided to demonstrate the effectiveness of our finding. [ABSTRACT FROM AUTHOR]

In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities.

We consider a φ-rigidity property for divergence-free vector fields in the Euclidean n-space, where φ ⁢ (t) {\varphi(t)} is a non-negative convex function vanishing only at t = 0 {t=0}. We show that this property is always satisfied in dimension n = 2 {n=2} , while in higher dimension it requires some further restriction on φ. In particular, we exhibit counterexamples to quadratic rigidity (i.e. when φ ⁢ (t) = c ⁢ t 2 {\varphi(t)=ct^{2}}) in dimension n ≥ 4 {n\geq 4}. The validity of the quadratic rigidity, which we prove in dimension n = 2 {n=2} , implies the existence of the trace of a divergence-measure vector field ξ on an ℋ 1 {\mathcal{H}^{1}} -rectifiable set S, as soon as its weak normal trace [ ξ ⋅ ν S ] {[\xi\cdot\nu_{S}]} is maximal on S. As an application, we deduce that the graph of an extremal solution to the prescribed mean curvature equation in a weakly-regular domain becomes vertical near the boundary in a pointwise sense. [ABSTRACT FROM AUTHOR]