We establish a local boundedness estimate for weak subsolutions to doubly nonlinear parabolic fractional p-Laplace equation. Our argument relies on energy estimates and nonlocal version of De Giorgi’s method. Furthermore, by means new algebraic inequality, we show that positive supersolutions satisfy reverse Hölder inequality. Finally, also prove logarithmic decay supersolutions.

Abstract We establish some interesting refinements of the $(p,q)$ ( p , q ) -Hölder integral inequality and -power-mean inequality. As applications, we show that existing -integral inequalities can be improved by results obtained in this paper.

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...

Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain including extended type Gauss hypergeometric function confluent function, respectively, virtue Hölder integral inequality Chebyshev’s inequality. We also studied monotonicity, log-concavity, log-convexity functions, which are deri...

Abstract We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove Sobolev-type inequality, weak Harnack local Hölder estimate.

In the paper, with help of two known integral identities and by virtue classical Hölder inequality, authors establish several new inequalities Hermite–Hadamard type for convex functions. These newly established generalize some results.

In this paper, we give converses of the Jensen and Edmundson– Lah–Ribarič inequalities which are more accurate than the existing ones. These converses are given in a difference form and they rely on the recent refinement of the Jensen inequality obtained via linear interpolation of a convex function. As an application, we also derive improved converse relations for generalized means, for the Hö...

A new constantWD(X) is introduced into any real 2n-dimensional symmetric normed space X . By virtue of this constant, an upper bound of the geometric constant D(X), which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrarym-dimensional symmetric normed linear space (m≥ 2). As an application, the result is...

We study the existence, uniqueness and rate of decay of correlation of equilibrium measures associated to robust classes of non-uniformly expanding local diffeomorphisms and Hölder continuous potentials. The approach used in this paper is the spectral analysis of the Ruelle-PerronFrobenius transfer operator. More precisely, we combine the expanding features of the eigenmeasures of the transfer ...