Document Details

Document Type : Thesis 
Document Title :
BEST PROXIMITY POINTS AND FIXED POINTS FOR NONLINEAR MAPPINGS
أفضل النقط القــرابية والنقاط الثابتة للرواسم غير الخطية
 
Subject : Faculty of Sciences 
Document Language : Arabic 
Abstract : Some basic concepts and notions of functional analysis are recalled. A brief discussion on Pompeiu-Hausdorff metric and multivalued mappings are included. Various fixed point theorems for singlevalued as well as multivalued contraction, nonexpansive, continuous and upper semicontinuous mappings are stated. Some salient features of the set of best approximations and metric projection are highlighted. Several notions and results on best proximity points are also presented. A short proof of a recent result is given. The existence of a best proximity point of a multivalued upper semicontinuous mapping which commutes with a singlevalued relatively u-continuous mapping is established. A common fixed point result for commuting affine relatively u-continuous mappings and an extended version of the Markov-Kakutani theorem for best proximity points are given in strictly convex Banach spaces. A best proximity point theorem is obtained for a multivalued upper semicontinuous mapping which commutes with a family of commuting affine relatively u-continuous mappings. Using the method of asymptotic centers, a best proximity point result is proved for multivalued nonexpansive mappings having a noncompact domain. The existence of a best proximity point is shown in proximinal pair of sets for multivalued upper semicontinuous or nonexpansive mappings. Best proximity points of multivalued nonexpansive mappings in starshaped sets are also studied. 
Supervisor : Prof. Dr. Naseer Shahzad Ayub 
Thesis Type : Doctorate Thesis 
Publishing Year : 1438 AH
2017 AD 
Co-Supervisor : Dr. Maryam Alghamdi 
Added Date : Thursday, June 8, 2017 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
غادة نايف النمرAlNemer, Ghada NaifResearcherDoctorate 

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