Search Results (219)

In this paper, we investigate reverse Hardy-type inequalities associated with generalized weighted fractional kernel operators. The introduced operator framework unifies several important classes of integral operators, including classical Hardy operators, weighted Riemann–Liouville fractional integrals and generalized k-fractional operators. Using weighted kernel techniques, Hölder-type estimates and operator-theoretic methods, we establish new reverse Hardy inequalities involving mixed integrability parameters in weighted Lebesgue spaces. In addition, sufficient conditions for the boundedness of the corresponding fractional kernel operators are obtained. Several classical inequalities are recovered as particular cases of the developed framework. We also investigate the asymptotic behavior and near-optimality of the obtained constants by means of explicit power-type examples. Furthermore, applications to fractional integral equations and generalized weighted kernel operators are presented. The results obtained in this paper provide a unified approach to reverse Hardy inequalities for weighted fractional kernels and extend several existing results from the literature. Full article

This paper establishes a new general integral identity for differentiable functions involving weighted fractional integral operators. By applying this identity together with s-convexity and s-uniform convexity with modulo $\Phi$, we derive several refined Hermite–Hadamard inequalities. Our results generalize and unify multiple classical and recent inequalities reported in the literature, which are recovered as special cases under a specific weighting selection. Furthermore, we demonstrate the applicability of the established bounds through concrete evaluations involving special means of real numbers, the q-digama function, and the modified Bessel function. Finally, our theoretical bounds are validated using 2D/3D visual representations and numerical simulations. Full article

Symmetric quantum calculus offers a dynamic framework for investigating the various classes of functions. However, the symmetric quantum operators become inconclusive at certain points. To overcome the limitations of existing calculi, operators over finite intervals have been extensively explored. To develop a more general and applicable setup, we introduce the symmetric quantum derivative and integral operators governed by an arbitrary point. Furthermore, we discuss structural properties of the newly developed operators and special cases to relate to the existing literature. Then, by applying the concepts of general symmetric quantum operators, convexity, Lipschitzian property, and Korkine’s identity, we derive a new set of inequalities, including Hermite–Hadamard, Ostrowski, Hólder, Minkowski, and Gruss-type inequalities, respectively. The proposed inequalities are useful to derive the bounds of generalized symmetric quantum integrals. Furthermore, the newly developed operators can be applied to study the impulsive difference equations and their dynamics. Additionally, a feed-forward ANN model is established to approximate the analytic expressions involved in inequalities and to observe the consistency of integral bounds. The results of the ANN analysis suggest a significant agreement between analytical solutions and approximations. Lastly, we focus on an applicable analysis of our derived results. The generic nature of operators will lead to new developments in quantum calculus. The hybrid approach evolved in this study will bring new applicable insights to the mathematical analysis. Full article

In this paper, we present new refinements of the generalized versions of Hölder’s inequality. Such refinements are rare. Our results are novel and clearly illustrate the essence of some recent specific refinements. As for applications, we present new inequalities for integral power means, give a new refinement of the generalized Opial–Olech inequality, refine the well-known inequality between Rényi’s entropies with different parameters by utilizing the concept of “useful” information, and finally, we obtain a refinement of the Cauchy–Bunyakovsky–Schwarz inequality. Full article

Introduction: Globally, disabled individuals experience persistent social inequalities and health inequities, yet the health and wellbeing of Deaf, DeafBlind, blind, and partially sighted (DDBBPS) people remain profoundly under-researched and excluded from social science and health policy agendas. Existing studies narrowly focus on narratives of hearing and vision impairments within a medical model of disability, which pathologizes difference and obscures the biomedical origins of social inequalities and health inequities experienced by these groups. Methods: Drawing on critical disability studies and community-based literature, this narrative review introduces and applies the concept of medical violence to examine how systemic ableism, audism, and ocularcentrism shape DDBBPS people’s healthcare experiences. Results: We identify six interrelated manifestations of medical violence: denied interpreting services, inaccessible health communication, harmful interpersonal practices, health inequities and medical avoidance, absence of DDBBPS practitioners, and gaps in community-based care. Conclusions: These conditions reinforce a cycle of exclusion and misrepresentation, wherein DDBBPS persons are denied equitable access to healthcare and are simultaneously constructed as objects of cure rather than as knowledge holders. We argue for a community-based participatory research agenda led by and for DDBBPS communities to challenge ableist research paradigms and advance health equity. Full article

This paper establishes new Fejér and Hermite–Hadamard-type inequalities for functions of two variables whose mixed second-order partial derivatives satisfy coordinated GA-convexity or coordinated GA-quasi-convexity on a rectangle in the positive quadrant. Our main results are formulated for non-negative continuous weight functions that are not necessarily symmetric with respect to the geometric means of the interval endpoints, thereby extending the classical framework to genuinely asymmetric weights. However, to obtain explicit and sharp integral bounds in certain cases, we also employ a technical lemma that assumes a special symmetric setting where the weight function is symmetric on each coordinate with respect to $\sqrt{h_1{h}_2}$ and $\sqrt{k_1{k}_2}$. We clearly distinguish which theorems hold for general asymmetric weights and which depend on this symmetry condition. Our findings unify and extend numerous previously known results for both symmetric and non-symmetric weight functions. Full article

Let $L=-\Delta +V$ be a Schrödinger operator, where $\Delta$ is the Laplacian defined on ${\mathbb{R}}^n$ and the nonnegative potential V satisfies the reverse Hölder inequality. In this paper, we mainly establish weighted mixed weak-type endpoint estimates for Littlewood–Paley square functions associated with the heat semigroup $e^{-tL}$ and their commutators. Such inequalities not only provide a refined characterization of the endpoint behavior of these operators in weighted spaces—extending the classical weak $(1,1)$ bounds, but also have potential applications to the regularity theory of Schrödinger equations with non-smooth potentials and to the boundedness of spectral multipliers. Our approach is based on the Calderón–Zygmund decomposition adapted to Schrödinger setting, which allows for a direct proof without invoking the associated maximal operator. These results are new even in the unweighted setting, and their weighted formulations offer a robust foundation for further developments in Fourier analysis and elliptic equations. Full article

In this paper, we introduce Atangana–Baleanu–tempered–conformable (ABTC) generalized integral operators and establish associated Milne–Mercer-type inequalities for differentiable convex functions. The proposed kernel simultaneously incorporates AB-type local–nonlocal mixing, exponential attenuation, and conformable distance scaling. Using a kernel-dependent integral identity together with the Jensen–Mercer inequality, convexity arguments, and Hölder’s inequality, we derive estimates whose coefficients depend jointly on the independent parameters $\theta$, $\alpha$, $\beta$, and $\lambda$. None of the corresponding AB–conformable, tempered–conformable, or AB-type tempered specializations retains all these mechanisms simultaneously. Parameter reductions recover several previously known integral settings and provide consistency checks for the construction. Numerical examples are included to illustrate the validity, comparative behavior, and parameter sensitivity of the resulting bounds. Full article

This work constructs a family of weighted higher-order Opial-type estimates on an arbitrary time scale $\mathbb{T}$, with the weight structure generated by a non-decreasing auxiliary function $\omega$ and its delta derivative ${\omega }^{\Delta }$. For n-times delta differentiable functions whose delta derivatives of orders $0,1,\dots ,n-1$ vanish at the left endpoint, the mixed functional ${\int }_a^b{v\left(t\right)|u\left(t\right)|}^p{|u^{{\Delta }^n}\left(t\right)|}^q\Delta t$ is bounded by expressions involving only the highest-order delta derivative $u^{{\Delta }^n}$. Three forms are obtained: a Hölder-type product estimate, a Young-type two-term estimate with a free balancing parameter $\theta >0$, and an optimized single-integral estimate with the explicit constant $K={(r-1)}^{1-1/r}/r$, where $r=(p+q)/q$. The proofs rely on the Taylor representation on time scales, Hölder’s inequality, Jensen’s inequality, and Fubini’s theorem. The resulting bounds are governed by computable kernels that encode the interaction between the Taylor monomials, the auxiliary weight, and the external weight. Specializations to $\mathbb{T}=\mathbb{R}$, $\mathbb{T}=\mathbb{Z}$, and the quantum lattice $q_0^{{\mathbb{N}}_0}$ recover classical, discrete, weighted, and quantum Opial inequalities with their standard constants and also yield several higher-order weighted estimates. As an application, a uniqueness criterion for higher-order dynamic initial value problems is established. Full article

This paper deals with a system of G-stochastic differential equations with jumps, driven by G-Brownian motion and the G-Lévy process. By using Burkholder–Davis–Gundy inequalities, we prove the moment estimate and the Hölder regularity of the solution, under the linear growth and the global Lipschitz conditions of the coefficients with respect to the state variable uniformly in the time variable. Moreover, different stability properties are proved. Some illustrative examples from finance are employed in order to support our theoretical results. Full article

This work is devoted to the analysis of the limit behavior of the solution to a class of fractional stochastic differential equations with Markovian switching and multiplicative fractional Brownian motion. With the aid of fractional calculus, generalized Riemann-Stieltjes integrals, stopping time techniques and inequality techniques, an averaging principle is established within the framework of Hölder continuous spaces. We prove that the solution of the original fractional Markovian jump system converges in the mean-square sense to that of the averaged equation, thereby justifying the averaging method as an effective technique for reducing the system’s complexity. Finally, concrete examples are presented to demonstrate our theoretical findings. Full article

This paper establishes a weighted Simpson-type identity on the parameter domain associated with quantum integral operators. Using this identity together with Hölder’s inequality and the power mean inequality, we derive new estimates for classes of functions whose associated parameter-domain q-derivatives satisfy h-convexity assumptions. Additional bounds are obtained under boundedness and Lipschitz conditions. Applications to the s-moment of a random variable and to several special means are derived in the classical limit $q\to 1^{-}$. Full article

The Hilfer fractional derivative effectively captures non-locality, historical dependence, and memory effects, making it valuable for modeling real-world systems, and exponential growth can describe explosive growth phenomena in real-world problems. This paper focuses on the existence of mild solutions for infinite-delay differential equations involving Hilfer fractional derivatives, fractional Laplacian operator ${(-\Delta )}^{\delta }$, and exponentially growing functions in Orlicz spaces. First, by utilizing standard $L^p$-$L^q$ estimates for strongly continuous semigroups generated by fractional Laplacian operator, the existence of global solutions in the Orlicz space $\exp L^p\left({\mathbb{R}}^d\right)$ and the time-weighted $L^z\left({\mathbb{R}}^d\right)$ space is established. Then, by leveraging Hölder’s interpolation inequality, the existence of local solutions in $L^1\left({\mathbb{R}}^d\right)\cap L^{\infty }\left({\mathbb{R}}^d\right)$ is established. Full article

In this paper, based on the Schauder fixed point theorem, the (generalized) Darbo fixed point theorem, and the (generalized) Banach contraction mapping principle, we study the mixed-type fractional impulse evolution equation with non-local and delay terms, and obtain the existence and uniqueness theorems under whether the operator is compact or not. The order of the derivative in this paper is $0<\alpha <1$, this fractional order introduces a series of problems concerning compactness, continuity, and convergence. We overcome these problems using methods such as Hölder inequality and Minkowski inequality. Moreover, under the condition of the non-compact measure, the non-negative constant is extended to an unbounded Lebesgue-integrable function. In addition, when obtaining the uniqueness of the solution through the (generalized) Banach contraction mapping principle, the non-negative constant L in the Lipschitz condition is extended to an unbounded Lebesgue integrable function. Finally, a case study is conducted to demonstrate the validity of the theoretical results. Full article

Background/Objectives: Women+ (e.g., women and individuals assigned female at birth) experience disproportionate health risks and persistent gaps in access to care. Women+ health research remains significantly underfunded and understudied, contributing to inequities in diagnosis, treatment, and outcomes. This study aims to collaboratively identify and prioritize the most pressing unanswered research questions related to women+ health in the Maritime provinces of Canada. Methods: This study will use a modified Priority Setting Partnership (PSP) methodology based on the James Lind Alliance framework. A mixed-methods participatory approach will be used, including bilingual online surveys (French, English) and a one-day consensus workshop. Participants will include women+, healthcare professionals, researchers, policymakers, and the public residing in the Maritime provinces (Nova Scotia, New Brunswick, and Prince Edward Island). An initial survey will collect research uncertainties through open-ended questions. A second survey will rank verified uncertainties, followed by a facilitated workshop to achieve consensus on the Top 10 research priorities. Descriptive statistics will summarize participant demographics. Anticipated Results: This project is expected to generate a collaboratively developed Top 10 list of research priorities for women+ health in the Maritimes, which will be used to prioritize future research related to women+ health. Conclusions: By centering women+ voices and engaging diverse interest holders, this study will establish a shared regional research agenda to guide future research, funding, and policy initiatives for women+ health research. Full article