33,154 Results Found

This paper investigates the composition structures of certain fractional integral operators whose kernels are certain types of generalized hypergeometric functions. It is shown how composition formulas of these operators can be closely related to the...

In this paper, two new integral operators are defined using the operator $D{R}_{\lambda }^{m,n}$, introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined...

The results contained in this paper are the result of a study regarding fractional calculus combined with the classical theory of differential subordination established for analytic complex valued functions. A new operator is introduced by applying t...

The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such...

We consider three new classes of meromorphic functions defined by an extension of the Wanas operator and two integral operators, in order to study some preservation properties of the classes. The purpose of the paper is to find the conditions such th...

We propose the definitions of some fractional integral operators called k-Atangana–Baleanu fractional integral operators. These newly proposed operators are generalizations of the well-known Atangana–Baleanu fractional integral operators....

In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize...

In this work, we explore the impact of integral operators such as the Libera and Alexander operators on specific families of analytic functions introduced in the literature and find some of their remarkable results. Using techniques from differential...

In this paper, we introduce the generalized left-side and right-side fractional integral operators with a certain modified ML kernel. We investigate the Chebyshev inequality via this general family of fractional integral operators. Moreover, we deriv...

The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding...

This article considers a general family of weighted fractional integral operators and utilizes this general operator to establish numerous reverse Minkowski inequalities. When it comes to understanding and investigating convexity and inequality, symm...

In the article, the authors present several inequalities of the Čebyšev type for conformable k-fractional integral operators.

We present some formulas for the norm, as well as the essential norm, of a product of composition and an integral operator between some Bloch-type spaces of analytic functions on the unit ball, in terms of given symbols and weights.

Firstly, Hilbert-type integral inequalities with best constant factors are established for two non-homogeneous kernels. Then, by utilizing the relationship between the Hilbert-type inequality and the integral operator of same kernel, the parameter co...

The role of fractional integral inequalities is vital in fractional calculus to develop new models and techniques in the most trending sciences. Taking motivation from this fact, we use multiple Erdélyi–Kober (M-E-K) fractional integral...

Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies of fractional calculus have become the subject of intensive research in historical and contemporary...

In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk....

We define new classes of meromorphic p-valent convex functions, respectively, meromorphic close-to-convex functions, by using an extension of Wanas operator in order to study the preservation properties of these classes, when a well-known integral op...

It is very well-known that the special functions and integral operators play a vital role in the research of applied and mathematical sciences. In this paper, our aim is to present sufficient conditions for the families of integral operators containi...

In the present paper, a new operator denoted by $D_z^{-\lambda }{L}_{\alpha }^n$ is defined by using the fractional integral of Sălăgean and Ruscheweyh operators. By means of the newly obtained operator, the subclass $S_n\left(\delta ,\alpha ,\lambda \right)$ of analytic functions in the unit disc is introduc...

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 aim of this paper is to numerically solve the first kind linear Fredholm and Volterra integral equations by using Modified Bernstein–Kantorovich operators. The unknown function in the first kind integral equation is approximated by using the...

In this article, we utilize recent generalized fractional operators to establish some fractional inequalities in Hermite–Hadamard and Minkowski settings. It is obvious that many previously published inequalities can be derived as particular cas...

Inequalities related to derivatives and integrals are generalized and extended via fractional order integral and derivative operators. The present paper aims to define an operator containing Mittag-Leffler function in its kernel that leads to deduce...

Let $(X,M,\mu )$ be a $\sigma$ -finite measure space and denote by $P\left(X\right)$ the $\mu$ -measurable functions $f:X\to [0,\infty ]$ , $f<\infty$ $\mu$ ae. Suppose $K:X\times X\to [0$...

In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms of fractional integral operators. Based on this new identity, some generalized Bullen-type inequalities are obtained by employing conv...

Super-homogeneous functions including homogeneous functions, quasi-homogeneous functions, and several non-homogeneous functions are considered. Using the weight function method, the construction conditions of Hilbert-type multiple integral inequaliti...

In this paper, the authors introduce the Orlicz spaces corresponding to the Young function and, by virtue of the equivalent theorem between the modified K-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems fo...

In this paper, we obtain reverse Minkowski inequalities pertaining to new weighted generalized fractional integral operators. Moreover, we derive several important special cases for suitable choices of functions. In order to demonstrate the efficienc...

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral opera...

We consider a newly introduced integral operator that depends on an analytic normalized function and generalizes many other previously studied operators. We find the necessary conditions that this operator has to meet in order to preserve convex mero...

This paper contains a variety of new integral inequalities for $(s,m)$-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Cap...

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and gener...

We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (p-convexity, p-concavity, p-regularity) or, equivalently, some t...

In this paper, we address the lack of general Janowski-type subclasses for analytic functions involving higher-order q-derivatives, unifying cases with both positive and negative coefficients. Using a combination of higher-order q-derivative techniqu...

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 $(\alpha ,h-m)-p$-convexity is utilized frequently. In addition, a fracti...

In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications...

We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional...

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has...

An abstract convexity type is ${\mathbb{B}}^{-1}$–convexity. For ${\mathbb{B}}^{-1}$–convex functions, the Hermite–Hadamard inequality was previously found. Recently, however, new and more popular types of fractional integral operators have been develo...

In this paper, necessary and sufficient conditions are established for the boundedness and compactness of a weighted integral operator when acting between the weighted Bloch space ${\mathcal{B}}_{\mu }$ and the weighted Hardy space ${\mathcal{H}}_v^{\infty }$ on the Cartan–Harto...

In this paper, by adopting the classical method of proofs, we establish certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. The main results are more ge...

New results concerning fuzzy differential subordination theory are obtained in this paper using the operator denoted by $D_z^{-\lambda }{L}_{\alpha }^n$, previously introduced by applying the Riemann–Liouville fractional integral to the convex combin...

Complex Intuitionistic Fuzzy Sets (CIFSs) are an advanced form of intuitionistic fuzzy sets that utilize complex numbers to effectively manage uncertainty and hesitation in multi-criteria decision making (MCDM). This paper introduces the Shapley Choq...

In this work, we deal with the autonomy issue in the perturbation expansion for the eigenfunctions of a compact Hilbert–Schmidt integral operator. Here, the autonomy points to the perturbation expansion coefficients of the relevant eigenfunction not...

The aim of this article is to obtain new Hermite–Hadamard–Mercer-type inequalities using Raina’s fractional integral operators. We present some distinct and novel fractional Hermite–Hadamard–Mercer-type inequalities for the functions whose absolute v...

Integral inclusion systems play a significant role in applied analysis and modeling, providing an effective framework for studying various physical, engineering, and dynamical processes. In this work, the solvability of a multidimensional integral in...

This research aims to develop generalized fractional integral inequalities by utilizing multiple Erdélyi–Kober (E–K) fractional integral operators. Using a set of j, with $(j\in \mathbb{N})$ positively continuous and decaying functions in t...

In this paper, we use two new fractional integral operators with exponential kernel about the midpoint of the interval to construct some Hermite–Hadamard type fractional integral inequalities for h-convex functions. Taking two integral identiti...

In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parame...