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Open research questions in Mathematical Inequalities and Applications

56 unresolved questions extracted from the limitations and future-work sections of 554 Mathematical Inequalities and Applications papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • Few ranges are yet to be established, providing scope for future research. Graphical evidence is provided for the results, but more rigorous proofs may be needed.

    Inequalities involving a Ramanujan integral · 2026 · DOI

  • Further investigation of the Ramanujan integral's properties. Examination of the relation between the Ramanujan integral and other types of functions. Application of the Ramanujan integral's properties in various fields.

    Inequalities involving a Ramanujan integral · 2026 · DOI

  • The definition of l-gap convex functions is more complex than that of convex functions. The proof of the Jensen type inequality for l-gap convex functions is challenging.

    Jensen Type Inequality for L-Gap Convex Functions · 2026 · DOI

  • To establish a general implication from positivity and monotonicity to off-axis Fourier positivity. To study the applications of the result in number theory and mathematics.

    A Fourth-Logarithmic-Derivative Inequality for the Riemann Xi Kernel · 2026 · DOI

  • The paper identifies a gap in the implication from positivity and monotonicity to off-axis Fourier positivity. The result does not imply the Riemann Hypothesis.

    A Fourth-Logarithmic-Derivative Inequality for the Riemann Xi Kernel · 2026 · DOI

  • The need to correct secondary results in another paper. The lack of explicit dependence on α in the weight functions.

    A COLLECTION OF SIX TWO-PARAMETER FAMILIES OF CYCLIC INEQUALITIES · 2026 · DOI

  • The mean-median-mode inequality has not been studied under a general definition of unimodality. Van ZWet's condition has not been interpreted in terms of stochastic ordering.

    Mean, Median, Mode III* · 1983 · DOI

  • To study the mean-median-mode inequality under different definitions of unimodality. To apply the results to real-world problems.

    Mean, Median, Mode III* · 1983 · DOI

  • The relationship between the Lipschitz constant ˆL in Theorem 3.20 and the structural properties of n-polynomial pre-invex functions deserves deeper investigation.

    On Novel Extension of n-Polynomial Pre-invex Functions and Related Post-Quantum Integral Inequalities with Application · 2026 · DOI

  • Remark 3.19 notes that geometrical growth begins in the right-hand side when ˆA, ˆB ≥ 1, suggesting potential limitations in the inequality's tightness that warrant further investigation.

    On Novel Extension of n-Polynomial Pre-invex Functions and Related Post-Quantum Integral Inequalities with Application · 2026 · DOI

  • The classical theory of Hilbert-type inequalities lacks richer analytical frameworks. The paper identifies a gap in the existing literature on Hilbert-type integral inequalities.

    Study of Two New Hilbert-Type Integral Inequalities with Arctangent-Maximum-Geometric Mean Kernel Functions · 2026 · DOI

  • The need for a new integral identity based on Riemann-Liouville fractional operators. The lack of applications of fractional corrected dual Euler-Simpson inequalities to inequalities involving different types of means.

    Some Fractional Corrected Dual Euler-Simpson Type Inequalities for Differentiable Strongly Preinvex Functions · 2026 · DOI

  • Further study of the spherical Schatten p-norm for operator tuples. Exploration of applications in quantum mechanics and other areas of operator theory.

    On inequalities involving the spherical operator transforms · 2026 · DOI

  • A gap in the literature on operator norm inequalities is identified. Prior work does not consider the spherical Schatten p-norm for operator tuples.

    On inequalities involving the spherical operator transforms · 2026 · DOI

  • Further research could explore the applications of the established inequalities. Further research could investigate the extensions of the results to other contexts.

    Affine Logarithmic HLS and Beckner-Type Logarithmic Sobolev Inequalities · 2026 · DOI

  • The authors identify a gap in the existing literature on affine inequalities. The authors aim to fill this gap by establishing an affine logarithmic HLS inequality and an affine version of Beckner's logarithmic Sobolev inequality.

    Affine Logarithmic HLS and Beckner-Type Logarithmic Sobolev Inequalities · 2026 · DOI

  • The paper identifies a gap in the literature on Bernstein inequalities on the unit ball. The paper aims to fill this gap by establishing new Bernstein inequalities.

    On Bernstein Inequalities on the Unit Ball · 2026 · DOI

  • Exploring multidimensional analogues. Extending the method to other classes of oscillatory kernel functions. Investigating potential applications in harmonic analysis and mathematical physics.

    On a specific ratio-cosine Hardy-Hilbert-type integral inequality in the entire plane · 2026 · DOI

  • There is a need to extend the Hardy-Hilbert-type integral inequalities to the entire plane. The question of the optimality of the constant factor π remains unanswered.

    On a specific ratio-cosine Hardy-Hilbert-type integral inequality in the entire plane · 2026 · DOI

  • The paper suggests several directions for future research, including the extension of fractional Hermite-Hadamard type inequalities to weighted settings. The study proposes the exploration of other generalized classes of convex functions beyond the m-convex class. The results can be adapted to the discrete setting, providing analogous inequalities in discrete calculus.

    Generalization and refinement of fractional Hermite-Hadamard type inequalities for m-convex functions · 2026 · DOI

  • The extension of the main results in case of other fractional integrals remains open. The paper identifies a gap in the generalization of some existing results.

    Hermite-Hadamard type inequalities via \((h,m)\)-convexity · 2026 · DOI

  • Future research can focus on extending the results to other types of convex functions. Future research can focus on applying the results to other areas of mathematics. Future research can focus on deriving new inequalities using the results presented in the paper.

    Jensen-Type Inequalities for Divided Differences via Generalized Convex Functions · 2026 · DOI

  • The paper identifies a gap in the existing literature regarding Jensen-Type Inequalities for Divided Differences via Generalized Convex Functions. The paper aims to fill this gap by deriving an estimate for Jensen’s inequality in the context of divided differences using (m+4)-convex functions.

    Jensen-Type Inequalities for Divided Differences via Generalized Convex Functions · 2026 · DOI

  • There is a need for a generalization of convex functions. The existing definitions of convex functions are not sufficient to model certain real-world problems.

    Jensen Type Inequality for L-Gap Convex Functions · 2026 · DOI

  • The paper suggests potential extensions to Hilbert space operators and matrix means inequalities. Further research can focus on applying the results to various fields, such as linear algebra and operator theory.

    Mean inequalities for norms and singular values · 2026 · DOI

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56 open questions have been extracted from the limitations and future-work passages of 554 Mathematical Inequalities and Applications papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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