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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

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