This paper deals with the concepts of upper and lower (τ 1 , τ 2 )-precontinuous multifunctions. Some characterizations of upper and lower (τ 1 , τ 2 )-precontinuous multifunctions are investigated. The relationships between upper and lower (τ 1 , τ 2 )-precontinuous multifunctions and the other types of continuity are discussed.Keywords: τ 1 τ 2 -preopen, upper (τ 1 , τ 2 )-precontinuous multifunction, lower (τ 1 , τ 2 )-precontinuous multifunction.

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We introduce the notion ofℳ𝒜(i,j)-continuous functions and some other forms of continuity in biminimal structure spaces. Some new characterizations and several fundamental properties ofℳ𝒜(i,j)-continuous functions are obtained.

Four types of numerical methods namely: Natural Cubic Spline, Special A-D Cubic Spline, FTCS and Crank–Nicolson are applied to both advection and diffusion terms of the one-dimensional advection-diffusion equations with constant coefficients. The numerical results from two examples are tested with the known analytical solution. The errors are compared when using different Peclet numbers.

This paper deals with the concepts of upper and lower almost β(Λ, sp)-continuous multifunctions. More-over, several characterizations concerning upper and lower almost β(Λ, sp)-continuous multifunctions are investi- gated.