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Operator Inequalities Involved Wiener–Hopf Problems in the Open Unit Disk

In: Differential and Integral Inequalities

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  • Rabha W. Ibrahim

    (University of Malaya)

Abstract

In this effort, we employ some of the linear differential inequalities to achieve integral inequalities of the type Wiener–Hopf problems (WHP). We utilize the concept of subordination and its applications to gain linear integral operators in the open unit disk that preserve two classes of analytic functions with a positive real part. Linear second-order differential inequalities play a significant role in the field of complex differential equations. Our study is based on a neighborhood containing the origin. Therefore, the Wiener–Hopf problem is decomposed around the origin in the open unit disk using two different classes of analytic functions. Moreover, we suggest a generalization for WHP by utilizing some classes of entire functions. Special cases are given in the sequel as well. A necessary and sufficient condition for WHP to be averaging operator on a convex domain (in the open unit disk) is given by employing the subordination relation (inequality).

Suggested Citation

  • Rabha W. Ibrahim, 2019. "Operator Inequalities Involved Wiener–Hopf Problems in the Open Unit Disk," Springer Optimization and Its Applications, in: Dorin Andrica & Themistocles M. Rassias (ed.), Differential and Integral Inequalities, pages 423-433, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-27407-8_13
    DOI: 10.1007/978-3-030-27407-8_13
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