Different limits of function sequence

Write a function convergenceFunc(fn, f, a, b, n, convType) that takes as input arguments: a function fn(n,x), fn(n,x) = f_n(x) - and a function f considered as the limit of the sequence f_n(x) on [a,b] in the sense given by the string convType: it can be pointwise convergence, uniform convergence, mean-square convergence.

And at this point I am a bit puzzled, since I want to enter only fn(n,x) and write matlab function, whichtake fn and find limits in different senses according to convType. But I dont know what to chage in limit to obtain different funcions for different types of convergeance.

[Torsten]

And what is the function "convergenceFunc" supposed to do ? Check whether f is correctly given for the convType ?

[Andrei]

It should animate fn convergence, frame by frame approach to f (depending on convType)

[Torsten]

And how should "convType" influence the animation ? Which convergence types are in the choice box ?

[Andrei]

For some functions there is only one type of convergeance - then convType can return error in case when expression doesnt convege in sense of convType. Also inside function I will evaluate errors which depend on convType

[Andrei]

I have written my realization, but it is no automized

clc
clear
close all

a = 0;
b = 1;
n = 10;

fn = @(n, x) (2.*x.*n + (-1).^n.*x^2)./n;
f = @(x) 2.*x;

% Uniform Convergence
convergenceFunc(@(n, x) (2.*x.*n + ((-1).^n).*x.^2)./n , @(x) 2.*x, a, b, n, 'uniform');

% Mean Squared Convergence
convergenceFunc(@(n, x) (2.*x.*n + ((-1).^n).*x.^2)./n , @(x) 2.*x, a, b, n, 'mean_squared');

% Pointwise Convergence
convergenceFunc(@(n, x) (2.*x.*n + ((-1).^n).*x.^2)./n , @(x) 2.*x, a, b, n, 'pointwise');

function convergenceFunc(fn, f, a, b, n, convType)
    
    x = linspace(a, b, 1000);  
    y_fn = zeros(1000, n);    
    y_f = f(x);               

    figure
    for i = 1:n
        y_fn(:, i) = fn(i, x);  

        
        if strcmp(convType, 'uniform')
            diff_metric = max(abs(y_fn(:, i) - y_f));
            title_str = 'Uniform Convergence';
        elseif strcmp(convType, 'mean_squared')
            diff_metric = sqrt(mean((y_fn(:, i) - y_f).^2));
            title_str = 'Mean Squared Convergence';
        elseif strcmp(convType, 'pointwise')
            diff_metric = NaN;
            title_str = 'Pointwise Convergence';
        end

        
        
        plot(x, y_fn(:, i), 'b', x, y_f, 'r');
        title(title_str);
        legend(['f_', num2str(i)], 'f');
        xlabel('x');
        ylabel('y');

        title(['Metric: ', num2str(diff_metric)]);

        drawnow;
        hold on

        pause(0.5);
    end
end