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In this paper, the variation of functions has been defined, whose domain is a convex and compact set in the plane. Furthermore, in addition to presenting properties that satisfy this variation, the vector space formed by functions with finite variation is studied, demonstrating that it is a Banach space and its elements can be expressed as the difference of non-decreasing functions. [ABSTRACT FROM AUTHOR]

In this article, the time to calculate the optimal height of the UAV is investigated as an important factor in determining the total flight time, energy consumption and total delay. In particular, in this paper, the calculation of the optimal height of the UAV, reducing the time of calculating the optimal height, reducing the energy consumption, reducing the total flight time and reducing the total delay is done. First, using the average path loss and UAV transmitted power functions, we present the optimal height of the UAV in the form of an optimization problem with a convex altitude range. Then, using the golden section search (GSS) algorithm and based on the condition of the function being unimodal, we calculate the optimization problem and obtain the optimal height value, which is the minimum of the average functions of the path loss and the transmitted power of the UAV. Also, using the convexity principle, we show that the average path loss function is convex in the mentioned interval. Next, using the relationship between the time to calculate the optimal height of the drone and the total flight time, we calculate the amount of energy consumed and the total delay. The simulation results using MATLAB show that the time to calculate the optimal height with the proposed algorithm is much faster than other methods. The time to calculate the optimal height in the proposed method is 0.03 s. The energy consumption using the proposed method is 53 kJ, and the flight time is 37 s, considering the stop on the way, which is the lowest value compared to other methods. Also, the total delay in the proposed method is less than in other methods. [ABSTRACT FROM AUTHOR]

The growth rate of a population serves as a measure of its Darwinian fitness, while its sensitivity indicates the intensity of selection. Generally, the sensitivity of r decreases with age, resulting in an expected increase in population mortality over time. However, this does not hold true for many populations, especially those exhibiting negative senescence. Both evolutionary entropy and its sensitivity serve as complementary measures for assessing fitness and the intensity of selection. The sensitivity of entropy is typically a convex function of age, implying stronger selection pressures in younger and older age groups. We show that the sensitivity functions of entropy exhibit a greater range of behaviours compared to those of the growth rate alone. This strongly suggests that evolutionary entropy offers an extremely valuable measure for capturing the diversity in aging patterns within populations, complementing what can be captured by the growth rate alone. [ABSTRACT FROM AUTHOR]

Generalizations of some Steffensen's inequalities for the class of higher order convex functions are obtained in present study. To prove the results, some preliminary lemmas are established by using extended Montgomery identities via Taylor's formula on time scales. Furthermore, Ostrowski type inequalities are also established, along with prove of optimization of the constant. Moreover, newly obtained results are discussed in discrete and quantum calculus as well. [ABSTRACT FROM AUTHOR]

In this paper, we are interested to prove some Hadamard and Fejér-Hadamard-type integral inequalities for m-convex functions via generalized fractional integral operator containing the generalized Mittag-Leffler function. In connection with we obtain some known results. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new concept "extended ((s1, m1)-(s2, m2))-convex function on co-ordinates" and establish some new inequalities of the Hermite-Hadamard type for extended ((s1, m1)-(s2, m2))-convex functions of 2 variables on co-ordinates. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce definitions of the (h1, h2)-GA-convex functions and the (h1, h2, m)-GA-convex functions, discuss some properties of these kinds of functions, establish some integral inequalities for these functions, and apply these inequalities to construct several more inequalities. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate upper bounds on the third Hankel determinants for the starlike and convex functions with respect to symmetric points in the open unit disk. [ABSTRACT FROM AUTHOR]

In the paper, the authors establish some new Hermite-Hadamard type inequalities for differentiable co-ordinated convex functions of two variables. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce the notion "logarithmically h-preinvex functions", reveal that the class of h-preinvex functions include several new and known classes of preinvex functions, and establish several integral inequalities of Hermite-Hadamard type. [ABSTRACT FROM AUTHOR]

In this paper, we prove Jensen’s inequality for diamond integrals on time scales and generalize this inequality for 2n-convex functions via Lidstone’s polynomials. Bounds for Čhebyšhev functional, Grüss-type inequality and Ostrowaski-type inequality related to Jensen’s type functional are also given in the paper. Moreover, our results are valid if we replace diamond integrals with delta integrals, nabla integrals or -diamond integrals on time scales as well (being special cases). [ABSTRACT FROM AUTHOR]

In this paper, we prove a version of the Hadamard inequality for function f such that is convex via k-fractional Caputo derivatives. Using convexity of , we find the bounds of the difference of fractional differential inequality. Also we have found inequalities for Caputo fractional derivatives. [ABSTRACT FROM AUTHOR]