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In this paper, we solve the question completely raised by Feng Qi and Dongkyu Lim in paper "Monotonicity properties for a ratio of finite many gamma functions" published in Advances in Difference Equations and get some properties about ratios of finitely many gamma functions such as complete monotonicity, logarithmically complete monotonicity, the Bernstein function property, null point and extreme value. [ABSTRACT FROM AUTHOR]

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided. [ABSTRACT FROM AUTHOR]

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, we introduce a biparametrized multiplicative integral identity and employ it to establish a collection of inequalities for multiplicatively convex mappings. These inequalities encompass several novel findings and refinements of established results. To enhance readers' comprehension, we offer illustrative examples that highlight appropriate choices of multiplicatively convex mappings along with graphical representations. Finally, we demonstrate the applicability of our results to special means of real numbers within the realm of multiplicative calculus. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of strongly generalized convex functions which is called as strongly η-convex stochastic processes. We prove the Hermite-Hadamard, Ostrowski type inequality, and obtain some important inequalities for above processes. Some previous results are special cases of the results obtained in this paper. [ABSTRACT FROM AUTHOR]

The Ruscheweyh derivative operator is used in this paper to introduce and investigate interesting general subclasses of the function class Σ m of m-fold symmetric bi-univalent analytic functions. Estimates of the initial Taylor-Maclaurin coefficients | a m + 1 | and | a 2 m + 1 | are obtained for functions of the subclasses introduced in this study, and the consequences of the results are discussed. Additionally, the Fekete-Szegö inequalities for these classes are investigated. The results presented could generalize and improve some recent and earlier works. In some cases, our estimates are better than the existing coefficient bounds. Furthermore, within the engineering domain, the utilization of the Ruscheweyh derivative operator can encompass a broad spectrum of engineering applications, including the robotic manipulation control, optimizing optical systems, antenna array signal processing, image compression, and control system filter design. It emphasizes the potential for innovative solutions that can significantly enhance the reliability and effectiveness of engineering applications. [ABSTRACT FROM AUTHOR]

In its additive version, Bohr–Mollerup's remarkable theorem states that the unique (up to an additive constant) convex solution f(x) to the equation Δ f (x) = ln x on the open half-line (0 , ∞) is the log-gamma function f (x) = ln Γ (x) , where Δ denotes the classical difference operator and Γ (x) denotes the Euler gamma function. In a recently published open access book, the authors provided and illustrated a far-reaching generalization of Bohr–Mollerup's theorem by considering the functional equation Δ f (x) = g (x) , where g can be chosen from a wide and rich class of functions that have convexity or concavity properties of any order. They also showed that the solutions f(x) arising from this generalization satisfy counterparts of many properties of the log-gamma function (or equivalently, the gamma function), including analogues of Bohr–Mollerup's theorem itself, Burnside's formula, Euler's infinite product, Euler's reflection formula, Gauss' limit, Gauss' multiplication formula, Gautschi's inequality, Legendre's duplication formula, Raabe's formula, Stirling's formula, Wallis's product formula, Weierstrass' infinite product, and Wendel's inequality for the gamma function. In this paper, we review the main results of this new and intriguing theory and provide an illustrative application. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce four new generalized quantum integrals of two variables functions which are called T q -integrals. We also give some examples of each of these given integrals. Then we establish corresponding T q -Hermite–Hadamard type inequalities for co-ordinated convex functions. In order to show correctness of our results, we apply our main theorems to several co-ordinated convex functions. [ABSTRACT FROM AUTHOR]

The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the Hölder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation. [ABSTRACT FROM AUTHOR]

In this paper we introduce necessary and sufficient conditions for a real-valued function to be preinvex. Some properties of preinvex functions and new versions of Jensen's integral type inequality in this setting are given. Several examples are also involved. [ABSTRACT FROM AUTHOR]

The dynamical behaviour of the (4+1)-dimensional fractional Fokas equation is investigated in this paper. The modified auxiliary equation method and extended (G ′ G 2) -expansion method, two reliable and useful analytical approaches, are used to construct soliton solutions for the proposed model. We demonstrate some of the extracted solutions used the definition of the truncated M-derivative (TMD) to understand its dynamical behaviour. The hyperbolic, periodic, and trigonometric function solutions are used to derive the analytical solutions for the given model. As a result, dark, bright, and singular solitary wave solitons are obtained. We observe the fractional parameter impact of the above derivative on the physical phenomena. Each set of travelling wave solutions have a symmetrical mathematical form. Last but not least, we employ Mathematica to produce 2D and 3D figures of the analytical soliton solutions to emphasize the influence of TMD on the behaviour and symmetry of the solutions for the proposed problem. The physical importance of the solutions found for particular values of the combination of parameters during the representation of graphs as well as understanding of physical incidents. [ABSTRACT FROM AUTHOR]

Unfortunately, eleven of our provinces were severely affected due to two severe earthquakes that occurred in our country, the Republic of Turkey, on February 6, 2023. As a result, thousands of buildings were destroyed and tens of thousands of our citizens lost their lives. From past to present, such disasters have occurred in many parts of our world and will continue to happen. In order to raise awareness for researchers and academicians reading our article, we will give a new definition of convexity in this article, and we will call it "earthquake convexity". In this paper, we study some algebraic properties of the earthquake convexity. Then we compare the results obtained with both Hölder, Hölder–İşcan inequalities and power-mean, improved power-mean integral inequalities and show that the results obtained with Hölder–İşcan and improved power-mean inequalities are better than the others. Some applications to special means of real numbers are also given. [ABSTRACT FROM AUTHOR]

The class of geometrically convex functions is a rich class that contains some important functions. In this paper, we further explore this class and present many interesting new properties, including fundamental inequalities, supermultiplicative type inequalities, Jensen-Mercer inequality, integral inequalities, and refined forms. The obtained results extend some celebrated results from the context of convexity to geometric convexity, with interesting applications to numerical inequalities for the hyperbolic and exponential functions. [ABSTRACT FROM AUTHOR]

In this paper, a new integral identity is provided. Based on this equality, Simpson-type dual integral inequalities for functions whose first derivatives are s-convex via Riemann–Liouville fractional integrals are established. [ABSTRACT FROM AUTHOR]

In the last two decades, several properties of operators that are weaker than monotonicity have received attention by researchers from many areas including mathematical economics, with the goal to develop new tools applicable in convex analysis and related topics. This paper puts in perspective notions that are extensions of monotoniticity but not beyond quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict quasimonotonicity and proper quasimonotonicity, and discusses systematically when the sum of two operators satisfying one of those properties, inherits the same property. The case of properly quasimonotone operators deserves a special attention since this notion, being stronger than quasimonotonicity, suffices to obtain many results, including the solvability of variational inequality problems. Several examples showing the optimality in some sense of our results, are presented. [ABSTRACT FROM AUTHOR]

We study the connections between the equation ∑ i = 1 n a i f (α i x + (1 - α i) y) = 0 and the corresponding inequality. ∑ i = 1 n a i f (α i x + (1 - α i) y) ≥ 0. At present, it is clear that linear functional equations should be solved with the use of the results due to L. Székelyhidi. We show that the simplest and most efficient way of dealing with the (continuous) solutions of linear inequalities of the above form is connected with the use of stochastic orderings tools. It will be shown that, in order to solve the inequality, we need to know the continuous solutions of the corresponding equation. In the last part of the paper, we obtain some simple but unexpected connections in the other direction. [ABSTRACT FROM AUTHOR]

We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas. [ABSTRACT FROM AUTHOR]

We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown. [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]

N-functions and their growth and regularity properties are crucial in order to introduce and study Orlicz classes and Orlicz spaces. We consider N-functions which are given in terms of so-called associated weight functions. These functions are frequently appearing in the theory of ultradifferentiable function classes and in this setting additional information is available since associated weight functions are defined in terms of a given weight sequence. We express and characterize several known properties for N-functions purely in terms of weight sequences which allows to construct (counter-) examples. Moreover, we study how for abstractly given N-functions this framework becomes meaningful and finally we establish a connection between the complementary N-function and the recently introduced notion of the so-called dual sequence. [ABSTRACT FROM AUTHOR]

The concept of strong F -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F -concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities. [ABSTRACT FROM AUTHOR]

It is well known that convexity theory and its generalization play an important role and have many applications in mathematical programming. In the previous article [2], the authors studied E-convex and semi-E-convex functions. In the present article, we deal with a class of E-quasiconvex functions and give a weak condition for a lower semi-continuous function on ℝn to be an E-quasiconvex function. [ABSTRACT FROM AUTHOR]

We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus. [ABSTRACT FROM AUTHOR]