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Entropy bump conditions for fractional maximal and integral operators

100%

Rahm R., Spencer S.

Concrete Operators

2016

tom 3

nr 1

112-121

We investigate weighted inequalities for fractional maximal operators and fractional integral operators.We work within the innovative framework of “entropy bounds” introduced by Treil–Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.

Third-order differential subordination and superordination involving a fractional operator

86%

Ibrahim R. W., Ahmad M. Z., Al-Janaby H. F.

Open Mathematics

2015

tom 13

nr 1

The third-order differential subordination and the corresponding differential superordination problems for a new linear operator convoluted the fractional integral operator with the Carlson-Shaffer operator, are investigated in this study. The new operator satisfies the required first-order differential recurrence (identity) relation. This property employs the subordination and superordination methodology. Some classes of admissible functions are determined, and these significant classes are exploited to obtain fractional differential subordination and superordination results. The new third-order differential sandwich-type outcomes are investigated in subsequent research.

Upper and lower bounds of integral operator defined by the fractional hypergeometric function

86%

Ibrahim R. W., Ahmad M. Z., Al-Janaby H. F.

Open Mathematics

2015

tom 13

nr 1

In this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.

Ograniczanie wyników

2 Open Mathematics

1 Concrete Operators

2 Ahmad M. Z.

2 Al-Janaby H. F.

2 Ibrahim R. W.

1 Rahm R.

1 Spencer S.

1 2016

2 2015

Wyniki wyszukiwania

Entropy bump conditions for fractional maximal and integral operators

Third-order differential subordination and superordination involving a fractional operator

Upper and lower bounds of integral operator defined by the fractional hypergeometric function