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The logarithmic coefficients $\unicode[STIX]{x1D6FE}_{n}$ of an analytic and univalent function $f$ in the unit disc $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ with the normalisation $f(0)=0=f^{\prime }(0)-1$ are defined by $\log (f(z)/z)=2\sum _{n=1}^{\infty }\unicode[STIX]{x1D6FE}_{n}z^{n}$. In the present paper, we consider close-to-convex functions (with argument 0) with respect to odd starlike functions and determine the sharp upper bound of $|\unicode[STIX]{x1D6FE}_{n}|$, $n=1,2,3$, for such functions $f$. [ABSTRACT FROM PUBLISHER]

Let S denote the class of all functions f(z) = z + ∈n=2∞ anzn analytic and univalent in the unit disk D. For f ∈ S, Zalcman conjectured that |a2n− a2n−1| ≤ (n − 1)2 for n ≥ 3. This conjecture has been verified for only certain values of n for f ∈ S and for all n ≥ 4 for the class C of close-to-convex functions (and also for a couple of other classes). In this paper we provide bounds of the generalized Zalcman coefficient functional |λa2n−a2n−1| for functions in C and for all n ≥ 3, where λ is a positive constant. [ABSTRACT FROM AUTHOR]

In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over Rn known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite–Hadamard type inequalities using the Jensen–Mercer inequality in the frame of q˙-calculus and majorized l-tuples. Firstly we derive q˙-Hermite–Hadamard–Jensen–Mercer (H.H.J.M) type inequalities with the help of Mercer’s inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q˙-differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q˙-identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper.

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0,π). We find bounds for |fz(z)|, and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction. [ABSTRACT FROM AUTHOR]

This paper explores a paradigm for producing geometrical algorithms in which logical decisions that depend on finite-precision numerical calculation cannot lead to failure. It applies this paradigm to the task of intersecting two convex polyhedral objects. A key tool in this work is a method of perturbing embedding polyhedra in ways consistent with their topology. [ABSTRACT FROM AUTHOR]

We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space \mathbb {H}^{n+1} (n\geq 2) with the speed given by arbitrary positive power \alpha of the Gauss curvature. We prove that if the initial hypersurface is convex, then the smooth solution of the flow remains convex and exists for all positive time t\in [0,\infty). Moreover, we apply a result of Kohlmann which characterises the geodesic ball using the hyperbolic curvature measures and an argument of Alexandrov reflection to prove that the flow converges to a geodesic sphere exponentially in the smooth topology. This can be viewed as the first result for non-local type volume preserving curvature flows for hypersurfaces in the hyperbolic space with only convexity required on the initial data. [ABSTRACT FROM AUTHOR]

The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function J λ , μ ν , m (z) : = Γ m (λ + 1) Γ (λ + μ + 1) 2 2 λ + μ z 1 − (ν / 2) − λ J λ , μ ν , m (z) , where the function J λ , μ ν , m satisfies the differential equation J λ , μ ν , m (z) : = (1 − 2 λ − ν) J λ , μ ν , m (z) + z (J λ , μ ν , m (z)) ′ with J ν , λ μ , m (z) = (z 2) 2 λ + ν ∑ k = 0 ∞ (− 1) k Γ m (k + λ + 1) Γ (k μ + ν + λ + 1) (z 2) 2 k for λ ∈ C ∖ Z − , Z − : = { − 1 , − 2 , − 3 , ... } , m ∈ N , ν ∈ C , and μ ∈ N 0 : = N ∪ { 0 } . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, 0 ≤ α < 1 . Ultimately, we discuss the starlikeness and convexity of order zero for J λ , μ ν , m , and it turns out that they are useful to extend the range of validity for the parameter λ to λ ≥ 0 where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates. [ABSTRACT FROM AUTHOR]

Symmetric derivatives and integrals are extensively studied to overcome the limitations of classical derivatives and integral operators. In the current investigation, we explore the quantum symmetric derivatives on finite intervals. We introduced the idea of right quantum symmetric derivatives and integral operators and studied various properties of both operators as well. Using these concepts, we deliver new variants of Young's inequality, Hölder's inequality, Minkowski's inequality, Hermite–Hadamard's inequality, Ostrowski's inequality, and Gruss–Chebysev inequality. We report the Hermite–Hadamard's inequalities by taking into account the differentiability of convex mappings. These fundamental results are pivotal to studying the various other problems in the field of inequalities. The validation of results is also supported with some visuals. [ABSTRACT FROM AUTHOR]

One of the classical problems concerns the class of analytic functions f on the open unit disk | z| < 1 which have finite Dirichlet integral Δ(1, f), where The class $${\mathcal{S} ^*(A,B)}$$ of normalized functions f analytic in | z| < 1 and satisfies the subordination condition $${zf'(z)/f(z)\prec (1+Az)/(1+Bz)}$$ in | z| < 1 and for some $${-1\leq B\leq 0}$$ , $${A \in \mathbb{C}}$$ with $${A\neq B}$$ , has been studied extensively. In this paper, we solve the extremal problem of determining the value of as a function of r. This settles the question raised by Ponnusamy and Wirths (Ann Acad Sci Fenn Ser AI Math 39:721-731, 2014). One of the particular cases includes solution to a conjecture of Yamashita which was settled recently by Obradović et al. (Comput Methods Funct Theory 13:479-492, 2013). [ABSTRACT FROM AUTHOR]

In this paper we will study the main properties of the set solutions of the paratingent equation (type differential inclusion) with delayed argument of the form: (Ptx)(t) ⊂ F([x]t) for t ≥ 0 with the initial condition: x(t) = ζ(t) for t ≤ 0. We will be interested particularly in the topological properties of emission and zone of emission. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of modifying the vertex weights of a block graph at minimum total cost so that a prespecified vertex becomes a 1-median of the perturbed graph. We call this problem the inverse 1-median problem on block graphs with variable vertex weights. For block graphs with equal edge lengths in each block, we can formulate the problem as a univariate optimization problem. By the convexity of the objective function, the local optimizer is also the global one. Therefore, we use the convexity to develop an $$O(M\log M)$$ algorithm that solves the problem on block graphs with M vertices. [ABSTRACT FROM AUTHOR]

The aim of the current paper is to obtain the sufficient conditions and inclusion relations for Pascal distribution series to be in some subclasses of Spiral-like functions in the open unit disk U. Further, we study an integral operator related to Pascal distribution series, and some consequences and corollaries of the main results are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we aim to state well-known Ostrowski inequality via fractional Montgomery identity for the class of $\phi-\lambda-$ convex functions. This generalized class of convex function contains other well-known convex functions from literature, allowing us to derive Ostrowski-type inequalities as specific instances. Moreover, we present Ostrowski-type inequalities for which certain powers of absolute derivatives are $\phi-\lambda-$ convex using various techniques, including Hölder's inequality and the power mean inequality. Consequently, various established results would be captured as special cases. Moreover, we provide applications in terms of special means, allowing us to derive many numerical inequalities related to special means from Ostrowski-type inequalities.

In this paper, we employ the theory of differential subordination to establish a theorem that delineates certain sufficient conditions for starlikeness, convexity, close-to-convexity, and quasi-convexity in relation to functions with fixed initial coefficients. Furthermore, we introduce some results derived from these conditions. Building upon this framework, we derive an extension of Nunokawa’s lemma for analytic functions with fixed initial coefficients.

In this paper we define generalized differential operators from some well-known operators on the class A(p) of analytic functions in the unit disk Δ = {z ∈ C : ΙzΙ < 1}. New class containing these operators is investigated. Also univalence of integral operator is considered [ABSTRACT FROM AUTHOR]

In this paper we consider the order of strongly starlikeness in the classes uniformly convex functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h -convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. [ABSTRACT FROM AUTHOR]

In 1984, Clunie and Sheil-Small constructed the harmonic Koebe functionexpecting it to play the role of extremal function for extremal problems over the class of sense-preserving harmonic univalent functions suitably normalized in the open unit disc. In this paper, we investigate the convolution properties of. In addition, we discuss the geometric properties of-starlike functions defined using the Sălăgean differential operator. Given a-starlike function, the productis shown to be univalent and convex in the direction of the real axis. [ABSTRACT FROM AUTHOR]

Lawrence Zalcman's conjecture states that if $${f(z)=z+\sum\nolimits_{n=2}^{\infty}a_{n}z^{n}}$$ is analytic and univalent in the unit disk $${|z|<1}$$ , then $${|a_n^2-a_{2n-1}|\leq (n-1)^2,}$$ for each $${n\geq 2}$$ , with equality only for the Koebe function $${k(z)=z/(1-z)^2}$$ and its rotations. This conjecture remains open although it has been verified for a few geometric subclasses of the class of univalent analytic functions. In this paper, we consider this problem for the family of normalized functions f analytic and univalent in the unit disk | z| < 1 satisfying the condition Functions satisfying this condition are known to be convex in some direction (and hence close-to-convex and univalent) in | z| < 1. A few other related basic results and remarks about the Hayman index of functions in this family are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we derive some Hermite-Hadamard type inequalities via s-convex functions of first and second sense respectively. These inequalities involve k-Riemann-Liouville fractional integrals. We also discuss some special cases. [ABSTRACT FROM AUTHOR]

In this paper we consider analytic functions in the unit disc D such that |f(p)(z)| is bounded in D. We present several sufficient conditions for function to be p-valent starlike, convex or strongly starlike of a certain order. [ABSTRACT FROM AUTHOR]

Researches in "point-free geometry", aiming to found geometry without using points as primitive entities, have always paid attention only to the logical aspects. In this paper, we propose a point-free axiomatization of geometry taking into account not only the logical value of this approach but also, for the first time, its educational potentialities. We introduce primitive entities and axioms, as a sort of theoretical guise that is grafted onto intuition, looking at the educational value of the deriving theory. In our approach the notions of convexity and half-planes play a crucial role. Indeed, starting from the Boolean algebra of regular closed subsets of ℝn, representing, in an excellent natural way, the idea of region, we introduce an n-dimensional prototype of point-free geometry by using the primitive notion of convexity. This enable us to define Re-half-planes, Re-lines, Re-points, polygons, and to introduce axioms making not only meaningful all the given definitions but also providing adequate tools from a didactic point of view. The result is a theory, or a seed of theory, suitable to improve the teaching and the learning of geometry. [ABSTRACT FROM AUTHOR]

High-quality convex colloidal photonic crystals can be grown on the tip of an optical fiber by self-assembly using the hanging drop method. They are convex-shaped, produce the diffraction of reflecting light with high efficiency (blazing colors), and have a high curvature. The convex colloidal crystals are easily detachable and, as free-standing objects, they are mechanically robust, allowing their manipulation and use as convex reflective diffraction devices in imaging spectrometers. Currently, the same characteristics are obtained by using gratings-based structures. The optical fiber/colloidal crystal interface is disordered; thus, no light diffraction can be registered. The ordering at this interface was highly increased by forming a polystyrene spacer on the optical fiber tip, which served as a self-assembly substrate for silica colloid, as a mechanical bond between the fiber and the crystal, and as a filler reservoir for an inverse-opal synthesis. The silica opal-like grown on the optical fiber tip can be transformed into a high-quality polystyrene (blazing colors) inverse-opal by using the polystyrene spacer as a filler. We found that the colloidal crystal axisymmetric self-assembles onto the optical fiber tip only if a maximum volume of the colloid drop is settled on a flat end of the polystyrene spacer. [ABSTRACT FROM AUTHOR]

The median location problem concerns finding locations of one or several new facilities that minimize the overall weighted distances from the existing to the new facilities. We address the problem of locating one new facility with a radius r on networks. Furthermore, the radius r is flexible and the objective function is the conic combination of the traditional 1-median function and the value r. We call this problem an extensive 1-median problem with radius on networks. To solve the problem, we first induce the so-called finite dominating set, that contains all points on the underlying network and radius values which are candidate for the optimal solution of the problem. This helps to develop a combinatorial algorithm that solves the problem on a general network G = (V,E) in O(|E||V|³) time. We also consider the underlying problem with improved algorithm on trees. Based the convexity of the objective function with variable radius, we develop a linear time algorithm to find an extensive 1-median with radius on the underlying tree. [ABSTRACT FROM AUTHOR]

Making use of Ruscheweyh derivative, we dene a new class of starlike functions of complex order subordinate to a conic domain impacted by Janowski functions. Coecient estimates and Fekete-Szego inequalities for the dened class are our main results. Some of our results generalize the related work of some authors. [ABSTRACT FROM AUTHOR]

Lap-time simulation is an important computational tool for many motor racing teams, but the assumption of ideal operating conditions and a ‘perfect’ racing driver is usually made. The aim of this paper is to extend lap-time simulation to include robustness to disturbances on the vehicle and robustness to mistakes by the driver. A previously developed receding-horizon model predictive control with a convex optimisation method for lap-time simulation is extended with a tube-based technique for robust model predictive control. A linear quadratic regulator compensatory controller maintains the vehicle close to the nominal vehicle path and speed trajectories in the presence of disturbances to the vehicle. An ensemble of disturbed trajectories defines a tube of trajectories, which is then used to modify the nominal vehicle path so that the track boundary constraints are satisfied in the presence of the disturbances. The lap time versus r.m.s. steering velocity curves for two different vehicle models demonstrate the expected trade-off: a decrease in the activity of the compensatory steering control increases the tube width, which leads to a longer lap time. The technique has application to designing and setting up cars to perform well in the presence of disturbances. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in. The main result is obtained for weights equal to a non-negative rational power of the absolute value of a special defining functionof the domain: we prove (weighted) Sobolev-and Lipschitz estimates for domains in(or, more generally, for domains having a Levi form of rankand for “decoupled” domains) and for convex domains. In particular, for these defining functions, we generalize results obtained by Bonami and Grellier and Chang and Li. We also obtain a general (weighted) Sobolev-estimate. [ABSTRACT FROM PUBLISHER]

SUMMARY This paper presents a reformulation of the original Matsuoka-Nakai criterion for overcoming the limitations which make its use in a stress point algorithm problematic. In fact, its graphical representation in the principal stress space is not convex as it comprises more branches, plotting also in negative octants, and it does not increase monotonically as the distance of the stress point from the failure surface rises. The proposed mathematical reformulation plots as a single, convex surface, which entirely lies in the positive octant of the stress space and evaluates to a quantity which monotonically increases as the stress point moves away from the failure surface. It is an exact reproduction, and not an approximated one, of the only significant branch of the original criterion. It is also suitable for shaping in the deviatoric plane the yield and plastic potential surfaces of complex constitutive models. A very efficient numerical algorithm for the implicit integration of the proposed formulation is presented, which enables the evaluation of the stress at the end of each increment by solving a single scalar equation, both for associated and non-associated plasticity. The algorithm can be easily adapted for other smooth surfaces with linear meridian section. Finally, a close expression of the consistent Jacobian matrix is given for achieving quadratic convergence in the external structural newton loop. It is shown that all this results in extremely fast solutions of boundary value problems. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we introduce new classes of analytic functions and we obtain sharp upper bounds of the functional |a3-ζa²2 |, for analytic functions belonging to these classes. [ABSTRACT FROM AUTHOR]

The interplay between topological hyperconvex spaces and sigma-finite measures in such spaces gives rise to a set of analytical observations. This paper introduces the Noetherian class of k-finite k-hyperconvex topological subspaces (NHCs) admitting countable finite covers. A sigma-finite measure is constructed in a sigma-semiring in a NHC under a topological ordering of NHCs. The topological ordering relation maintains the irreflexive and anti-symmetric algebraic properties while retaining the homeomorphism of NHCs. The monotonic measure sequence in a NHC determines the convexity and compactness of topological subspaces. Interestingly, the topological ordering in NHCs in two isomorphic topological spaces induces the corresponding ordering of measures in sigma-semirings. Moreover, the uniform topological measure spaces of NHCs need not always preserve the pushforward measures, and a NHC semiring is functionally separable by a set of inner-measurable functions. [ABSTRACT FROM AUTHOR]

In this paper the solutions of a second-order non-autonomous differential inclusion is discussed by means of some properties of set-valued mappings. The existence of solutions is established, and minimum and balance principles are obtained. [ABSTRACT FROM AUTHOR]

Abstract: If denotes the class of functions which are analytic and univalent in the unit disk , then the classical result of Szegö shows that every section of is univalent in . Exact (largest) radius of univalence of remains an open problem, although the corresponding results for sections of various geometric subclasses of have been obtained which include those for which holds in the unit disk. However, no attempt has been made to derive harmonic analog of these results. The central object in this case is the class of sense-preserving harmonic univalent mappings defined on the unit disk, normalized so that . Our primary objective in this paper is to solve the univalency of every section of a harmonic function in the class , where denotes the class of normalized univalent harmonic mapping in the unit disk satisfying the condition for , where and . In this paper, we first present sharp bounds for the moduli of the coefficients , of and then determine the value of so that the partial sums of are close-to-convex in . [Copyright &y& Elsevier]

In this paper, we propose and study new multivariate extensions of the dispersive, right-spread, decreasing mean residual life and new better than used in expectation univariate orders. These new orders are based on the comparison of univariate marginal distributions conditional on survival data for the rest of the components. Relationships among multivariate orders and applications to some multivariate random vectors are also provided. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a generalization of modified Salagean operator for harmonic univalent functions. We define a new subclass of complex-valued harmonic univalent functions by using this operator ,and we investigate necessary and sufficient coefficient conditions, distortion bounds, extreme points and convex combination for the above class of harmonic univalent functions. [ABSTRACT FROM AUTHOR]

In this paper we derive several subordination results for certain new classes of analytic functions defined by using Salagean operator. [ABSTRACT FROM AUTHOR]

Based on twin support vector machines (TWSVM) model, the twin support vector clustering (TWSVC) is a planar clustering model that increases inter-cluster separation. Because the TWSVC is not a standard model for some variables, its solving algorithm consumes lots of time and does not always converge to the optimal solution. To solve the problem, this paper proposes a novel clustering model, denoted as TWSVC+, based on twin support vector machines (TWSVM). The TWSVC+ is convex and standard with respect to each variable. Therefore, it is possible to solve this model rapidly with an algorithm that converges to a global optimal solution relative to each variable. The author presented linear TWSVC+ and non-linear TWSVC+ for clustering linear separable clusters and linear inseparable clusters, respectively. Experimental results on real datasets of UCI repository show that the TWSVC+ was better than TWSVC and support vector clustering (SVC) in accuracy and training time. [ABSTRACT FROM AUTHOR]

Partial sums of analytic univalent functions and partial sums of starlike have been investigated extensively by several researchers. In this paper, we investigate a partial sums of convex harmonic functions that are univalent and sense preserving in the open unit disk. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce some characterizations of (Gaussian) hypergeometric function to be in various subclasses of uniformly starlike and uniformly convex functions. Operators related to hypergeometric functions are also considered. Some of our results correct previously known results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide a result which concerns with the boundary behavior of analytic functions. It may be a local version of the well known Jack's lemma when we change the function normalization at the origin. [ABSTRACT FROM AUTHOR]

In the paper, by virtue of two new tools, the authors present the monotonicity and convexity of certain combinations of the complete elliptic integrals of the first kind, and obtain new sharp bounds and inequalities for them. [ABSTRACT FROM AUTHOR]

Abstract The geometric shape of vortex generator (VG) is an important contributory factor to heat transfer enhancement. In this paper, concave and convex curved delta winglet VGs in a channel of plate heat exchanger under laminar flow are studied and compared with the normal plane delta winglet VG to optimize the shape of VGs. The effects of the central angles ranging between 10° and 80° and the angles of attack (20°, 30°, 40°) of the concave and convex curved delta winglet VGs on the characteristics of heat transfer and pressure loss are presented for different Reynolds number (Re) ranging from 200 to 1400. The results showed that Nusselt number (Nu) increases with the increase in the central angle of the concave curved delta winglet VG, while Nu decreases with the increase in the central angle of the convex curved delta winglet VG. Comparing with the normal plane VG, the concave curved delta winglet VG is beneficial to heat transfer enhancement, while the convex curved delta winglet VG is disadvantageous to heat transfer enhancement. Optimum values of the central angle and the angle of attack exist for the concave curved delta winglet VG in terms of the best heat transfer performance. The largest values of Nu and surface goodness factor (JF) for the concave curved VG are larger by 19.7% and 11.35% respectively than those for the convex curved delta winglet VG in the studied range of parameters. Correlation equations for both Nu and friction factor (f) as a function of Re , central angle and angle of attack are presented for both concave and convex curved delta winglet VGs. Highlights • Concave and convex curved delta VGs are studied. • Effects of central angle and attack angle of VGs on heat transfer are presented. • Considerable heat transfer enhancement of concave curved VG is reported. • Correlation equations of Nu and f are proposed for both concave and convex curved VGs. [ABSTRACT FROM AUTHOR]

We investigate the problem of erroneous conformal area extracted by ray tracing in conformal structured mesh generation for the finite-difference time-domain method when tangential situations arise, referred to as corner singularity. The erroneous conformal area results from the fuzzification of intersecting length for tangential situations. Here, an effective mesh scheme to solve the corner singularity is proposed. In this scheme, additional degrees of freedom for mesh flags of vertexes and generalized consistency modification are proposed to solve the fuzzification of intersecting length, leading to accurate extraction of the conformal area. Furthermore, the scheme can tackle the convex and concave points uniformly without leading to possible breakdown of the conventional parity-number-based method. Rigorous and less rigorous staircase criteria are proposed to classify the cells accurately and effectively. The difficulties of concave point combined with the tangential situation are also successfully solved. Numerical examples of several microwave devices are given to show the validity of the proposed mesh scheme. [ABSTRACT FROM AUTHOR]

We introduce and study a comprehensive family of analytic univalent functions which contains various well-known classes of analytic univalent functions as well as many new ones. In this paper, we obtain coefficient bounds, distortion bounds and extreme points. Convolution conditions and convex combination are also determined for functions in this family. [ABSTRACT FROM AUTHOR]