In this paper, we give the generalized version of the quantum Simpson’s and quantum Newton’s formula type inequalities via quantum differentiable α,m-convex functions. The main advantage of these new inequalities is that they can be...
In this paper, the authors propose the notions of (α,s)-geometric-arithmetically convex functions and (α,s,m)-geometric-arithmetically convex functions, while they establish some new integral inequalities of the Hermite–Hadamard typ...
In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter m∈ 0,1. Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established...
Integral operators of a fractional order containing the Mittag-Leffler function are important generalizations of classical Riemann–Liouville integrals. The inequalities that are extensively studied for fractional integral operators are the Hada...
In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensio...
In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann&...
In this study, we examine the error bounds related to Milne-type inequalities and a widely recognized Newton–Cotes method, originally developed for three-times-differentiable convex functions within the context of Jensen–Mercer inequaliti...
Convex functions are studied very frequently by means of the Hadamard inequality. A symmetric function leads to the generalization of the Hadamard inequality; the Fejér–Hadamard inequality is one of the generalizations of the Hadamard in...
The main objective of this study is to establish two important right q-integral equalities involving a right-quantum derivative with parameter m∈[0,1]. Then, utilizing these equalities, we derive some new variants for midpoint- and trapezoid-typ...
This paper aims to obtain the bounds of a class of integral operators containing Mittag–Leffler functions in their kernels. A recently defined unified Mittag–Leffler function plays a vital role in connecting the results of this paper with...
Recently, there has been a strong push toward creating and expanding quadrature inequalities in quantum calculus. In order to investigate various avenues for quantum inquiry, a number of quantum extensions of midpoint estimations are studied. The goa...
This paper aims to study the bounds of k-integral operators with the Mittag-Leffler kernel in a unified form. To achieve these bounds, the definition of exponentially (α,h−m)−p-convexity is utilized frequently. In addition, a fracti...
In the frame of fractional calculus, the term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus and objective of this review paper is to present Hermite–Hadamard (H-H)-type inequalit...
A review of results on Hermite–Hadamard (H-H) type inequalities in quantum calculus, associated with a variety of classes of convexities, is presented. In the various classes of convexities this includes classical convex functions, quasi-convex...
In this study, we introduce the new subclasses, Mα(sin) and Mα(cos), of α-convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions t...
This article investigates inequalities for certain types of strongly convex functions by applying q-h-integrals. These inequalities provide the refinements of some well-known results that hold for (α,m)- and (ℏ-m)-convex and related functions. Inequa...
The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals ar...
Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability density functions over a measure space, (Χ,μ). Classical information geometry prescribes, on Μθ: (i) a Riemannian metric given by the Fisher informat...
Scholars from several disciplines have recently expressed interest in the field of fractional q-calculus based on fractional integrals and derivative operators. This article mathematically applies the fractional q-differential and q-integral operator...
Fractional integral operators are useful tools for generalizing classical integral inequalities. Convex functions play very important role in the theory of mathematical inequalities. This paper aims to investigate the Hadamard type inequalities for a...
The fractional integral is prolific in giving rise to interesting outcomes when associated with different operators. For the study presented in this paper, the fractional integral is associated with the convolution product of multiplier transformatio...
We introduce and analyze a subclass of analytic functions with negative coefficients, denoted by Pq,σm,ℓ,p(α,η), constructed through a generalized q-calculus operator in combination with a multiplier-type transformation. For thi...
The problem of conflict interaction between a group of pursuers and an evader in a finite-dimensional Euclidean space is considered. All participants have equal opportunities. The dynamics of all players are described by a system of differential equa...
This paper aims to establish generalized fractional integral inequalities for operators containing Mittag–Leffler functions. By applying (α,h−m)−p-convexity of real valued functions, generalizations of many well-known inequali...
In this paper, we define three subclasses Mp,αn,q(η,A,B),Ip,αn(λ,μ,γ),, Rpn,q(λ,μ,γ) connected with a q-analogue of linear differential operator Dα,p,Gn,q which consist of functions F of the form...
This study presents an innovative iterative method designed to approximate common fixed points of generalized contractive mappings. We provide theorems that confirm the convergence and stability of the proposed iteration scheme, further illustrated t...
In the past few years, many scholars gave much attention to the use of q-calculus in geometric functions theory, and they defined new subclasses of analytic and harmonic functions. While using the symmetric q-calculus in geometric function theory, ve...
The purpose of the paper is to present new q-parametrized Hermite–Hadamard-like type integral inequalities for functions whose third quantum derivatives in absolute values are s-convex and (α,m)-convex, respectively. Two new q-integr...
All-optical networks transmit messages along lightpaths in which the signal is transmitted using the same wavelength in all the relevant links. We consider the problem of switching cost minimization in these networks. Specifically, the input to the p...
We construct a family of linear optimal functional-repair regenerating storage codes with parameters {m,(n,k),(r,α,β)}={(2r−α+1)α/2,(r+1,r),(r,α,1)} for any integers r,α with 1≤α≤r, over any field...
This study provokes the existence of quantum Hermite-Hadamard inequalities under the concept of q-integral. We analyse and illustrate a new identity for the differentiable function mappings whose second derivatives in absolute value are (α,m) c...
The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Therm...