本文選題：偏矩度量空間 + 錐矩度量空間�。� 參考：《西南大學(xué)》2017年碩士論文

【摘要】：2000年Branciari在度量空間的基礎(chǔ)上,用四角不等式代替三角不等式提出了矩度量空間的概念,并證明了 Banach壓縮映象的不動點(diǎn)定理.隨后,許多學(xué)者將矩度量空間推廣為偏矩度量、錐矩度量、b-矩度量等空間,且在這些空間中研究了若干壓縮映象的不動點(diǎn).本文主要介紹一些廣義的矩度量空間的定義,并證明一些壓縮映象在這些空間中的不動點(diǎn)定理.共分為四部分:第一章,介紹一些矩度量空間的產(chǎn)生及其不動點(diǎn)理論研究概況,和本文主要研究內(nèi)容及意義.第二章,介紹偏矩度量空間的相關(guān)概念及弱(ψ,φ)壓縮映象研究近況,證明帶有四個自映象的弱(ψ,φ)壓縮映象映象在偏矩度量空間中的公共不動點(diǎn)定理.第三章,介紹錐矩度量空間的相關(guān)概念和多值映象的定義及發(fā)展近況,并證明一些多值映象在錐矩度量空間中的的不動點(diǎn)定理.第四章,介紹b-矩度量空間的概念及研究現(xiàn)狀,并研究b-矩度量空間中(ψ,φ)壓縮映象的不動點(diǎn)定理.
[Abstract]:In 2000, on the basis of metric space, Branciari proposed the concept of moment metric space by using four angle inequalities instead of trigonometric inequalities, and proved the fixed point theorem of Banach compression mappings. Then, many scholars extended the moment metric space into moment metric, cone moment measure, b- moment metric space, and studied some pressure in these spaces. The definition of some generalized moment metric spaces is introduced in this paper, and the fixed point theorems of some compressed mappings in these spaces are proved. The first chapter is divided into four parts: the first chapter introduces the production of some moment metric spaces and the research situation of the theory of fixed points, and the main research content and significance in this paper. The second chapter introduces the main contents and significance. The related concept of the moment metric space and the recent research on the weak () compression mappings, prove the common fixed point theorem with the weak (diameter, phi) mappings in the metric space. The third chapter introduces the concept of the cone moment metric space and the definition of the Multivalued Mappings and the recent development, and proves that some Multivalued Mappings are in the cone. The fixed point theorem in moment metric space. The fourth chapter introduces the concept and research status of b- moment metric space, and studies the fixed point theorem of the compressed mappings in the b- moment metric space.

【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O177.91;O189.11

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

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2 Fridoun MORADLOU;Peyman SALIMI;Pasquale VETRO;;SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES[J];Acta Mathematica Scientia;2013年04期

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本文編號：1808963