Pradhan, Dillip Kumar (2019) *On Maximal Monotone Operators and the Sum Problem in General Banach Spaces.* PhD thesis.

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## Abstract

Maximal monotone operators play an important role in non-linear modern analysis.

In this thesis, we focus on the most famous and significant open problem that is “Sumproblem” in monotone operator theory. First, we provide some powerful sufficient conditions for partial solutions of the Sum problem. The maximality of the sum of an ultramaximal monotone operator and a maximal monotone operator of type (D) with Br_ezis-Crandall-Pazy conditions in Grothendieck Banach spaces is established. Also, we work on Br_ezis-Haraux conditions in Grothendieck Banach spaces. Finally, a sufficient condition is provided for the convergence of a sequence of maximal monotone operators of type (D) in general Banach spaces. The representability of the lower limit of a sequence of maximal monotone operators of type (D) is discussed through their representative functions. Moreover, some conditions are given which guarantee the maximality of the lower limit of a sequence of maximal monotone operators of type (D).

Item Type: | Thesis (PhD) |
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Uncontrolled Keywords: | Monotone Operators; Maximal Monotone Operators; Sum Problems; (FPV)operator; type(FP); type(D); type(NI); Ultramaximal monotone operator; Convex function; Fitzpatrick function; Subdifferential operator; Normal cone; Rockafellar’s constraints; Sum theorem; Br_ezis-Crandall-Pazy conditions; Brezis-Haraux conditions; Graphical Convergence; Epi-convergence |

Subjects: | Mathematics and Statistics > Descrete Mathematics Mathematics and Statistics > Analytical Mathematics Mathematics and Statistics > Algebra Mathematics |

Divisions: | Sciences > Department of Mathematics |

ID Code: | 9856 |

Deposited By: | IR Staff BPCL |

Deposited On: | 05 Jul 2019 15:22 |

Last Modified: | 05 Jul 2019 15:22 |

Supervisor(s): | Pattanaik, Suvendu Ranjan and Pradhan, Seshadev |

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