On generalized variations (II)
On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions
Mathematics Subject Classification: 33D60, 33D90, 26A33Fractional q-integral operators of generalized Weyl type, involving generalized basic hypergeometric functions and a basic analogue of Fox’s H-function have been investigated. A number of integrals involving various q-functions have been evaluated as applications of the main results.
On gradients of functions definable in o-minimal structures
We prove the o-minimal generalization of the Łojasiewicz inequality , with , in a neighborhood of , where is real analytic at and . We deduce, as in the analytic case, that trajectories of the gradient of a function definable in an o-minimal structure are of uniformly bounded length. We obtain also that the gradient flow gives a retraction onto levels of such functions.
On Grande’s problem concerning functions
On granular derivatives and the solution of a granular initial value problem
Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s...
On Grüss like integral inequalities via Pompeiu's mean value theorem.
On Grüss type inequalities of Dragomir and Fedotov.
On Grüss type integral inequalities.
On H. Weyl and H. Minkowski polynomials.
On Hadamard integral inequalities involving two log-preinvex functions.
On Hadamard type inequalities for generalized weighted quasi-arithmetic means.
On Hadamard type polynomial convolutions with regularly varying sequences
On Hadamard's inequality on a disk.
On Hadamard-type inequalities involving several kinds of convexity.
On Hardy -inequalities
Some -analysis variants of Hardy type inequalities of the form with sharp constant are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.
On Hardy type inequality with non-isotropic kernels.
On Hardy-Hilbert integral inequalities with some parameters.
On Hardy-Hilbert's integral inequality.
On Hardy-Hilbert's integral inequality with parameters.
On Hardy's inequality in .