Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index.

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The Convenient Setting of Global Analysis

In this work we discuss some recent results about KKM mappings in cone metric spaces. We also discuss the fixed point existence results of multivalued mappings defined on such metric spaces. In particular we show that most of the new results are merely copies of the classical ones and do not necessitate the underlying Banach space nor the associated cone.

https://www.kau.edu.sa/Files/130/Researches/60219_31031.pdf

KKM mappings in metric type spaces

Publisher Summary This chapter discusses a few aspects of the role of differentials in nonlinear functional analysis. It presents a systematic exposition of several aspects of differential calculus in normed or topological linear spaces and highlights various settings in nonlinear functional analysis in which differentials play an important role. Differential splays at least three significant roles in the theory and application of nonlinear functional analysis. The first and the most familiar role is that of local approximation of a nonlinear map by a linear one. The differential is also important as a tool in nonlinear functional analysis. The third role of the differential is in the clue it provides for generalizations of a certain class of differentiable operators. The theory of differentiation in linear topological spaces is fairly complete for practical purpose.

Differentiability and Related Properties of Nonlinear Operators: Some Aspects of the Role of Differentials in Nonlinear Functional Analysis

Introduction 1. .4-proper mappings and fixed point theorems for Py-compact mappings 1.1 Basic facts about ^-proper mappings and approximation-solvability 1.2 Fixed point theory for ^-compact mappings 2. Equations involving linear ^-proper mappings 2.1 Approximation-solvability and bounded ^4-proper mappings 2.2 Equations involving unbounded linear mappings 2.3 Generalized Fredholm alternative 2.4 Dirichlet boundary value problem for elliptic equations 2.5 Stability of projective methods and ^4-properness 3. Equations involving nonlinear /4-proper mappings 3.1 Approximation-solvability and nonlinear ^4-proper mappings 3.2 Equations involving odd ^-proper mappings 3.3 Alternative for asymptotically linear mappings with applications to PDE 4. Generalized degree theory of ^-proper mappings and applications 4.1 Definition and properties of the generalized degree 4.2 Applications to some fixed point and mapping theorems 4.3 Fréehet differentiable and analytic type ^-proper mappings 5. Existence theorems and pseudo-v4-proper type mappings 5.1 Equations involving pseudo-y4-proper mappings 5.2 Application to fixed point and surjectivity theorems for (7-operators, IVcompact, weakly closed, and monotone type operators 5.3 Equations involving uniform limits of A-proper type mappings 5.4 Surjectivity theorems for odd limits of /4-proper mappings References

/pdf/on-the-approximation-solvability-of-equations-involving-a-4vvsbt3trr.pdf

On the approximation-solvability of equations involving $A$-proper and pseudo-$A$-proper mappings

In this review we describe the basic structure of positive continuous one-parameter semigroups acting on ordered Banach spaces. The review is in two parts.

Positive One-Parameter Semigroups on Ordered Banach Spaces

We prove that factor groups of cartesian powers of finite non-abelian simple groups cannot be countably infinite. This is not our main result, but it had been our original aim. The proof is based on a similar fact concerning er-complete Boolean algebras, and on a representation of certain subcartesian powers of a group in its group ring over a Boolean ring. This representation, to which we give the name \"Boolean power\", will be our central theme, and we begin with it.

Boolean powers of simple groups

https://msp.org/pjm/1984/110-2/pjm-v110-n2-p10-s.pdf

The Jordan decomposition and half-norms

/pdf/the-canonical-half-norm-dual-half-norms-and-monotonic-norms-4755fuix7o.pdf

The canonical half-norm, dual half-norms, and monotonic norms

The order structure of the space of all continuous linear operators on an ordered Banach space is studied. The main topic is the Robinson property, that is, the norm of a positive linear operator is attained on the positive unit cone.

/pdf/on-linear-operators-on-ordered-banach-spaces-1j3sdeql3z.pdf

On linear operators on ordered banach spaces

Let E be a real Banach space. The set of all continuous linear mappings of E into E is a Banach algebra under the usual algebraic operations and the operator bound as norm. We denote this Banach algebra by ℒ, if E is a separate Hilbert space .

/pdf/a-note-on-d-ideals-in-some-near-algebras-59ts2zdu3p.pdf

Sadayuki Yamamuro

Papers

Boolean powers of simple groups

The Jordan decomposition and half-norms

The canonical half-norm, dual half-norms, and monotonic norms

On linear operators on ordered banach spaces

A note on d -ideals in some near-algebras