In 2002, Császár [1] introduced the notions of generalized topology and generalized continuity. In 2008, Császár [3] defined an enlargement and construct the generalized topology induced by an enlargement; introduced the concept of (κ, λ)-continuity and (κμ, λμ)continuity on enlargements. In 2008, Császár [4] defined and studied the notions of product of generalized topologies. In 2010, S. Mara...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

The paper introduces a new generalized closed set via semi local function. Its relationship with other existing generalized closed sets are established. It’s basic properties are discussed. A new decomposition of continuity is derived. General Terms Ideal topological space, local function and semi-local function.

In this paper, using the Steklov function, we introduce the generalized continuity modulus and denethe class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.

In order to tackle the problem of shape design and shape adjustment of complex surfaces in engineering, continuity conditions between generalized Bézier-like surfaces with multiple shape parameters are studied in this paper. Firstly, the geometric model of the generalized Bézier-like surfaces is built by blending a number of Bézier-like curves with independent shape parameters. Secondly, based ...

The condition f(x + 2h) 2f(x + h) + f(x) = o(l) (as h -* 0) at each x is equivalent to continuity for measurable functions. But there is a discontinuous function satisfying 2f(x + 2h) f(x + h) f(x) = o(l) at each x. The question of which generalized Riemann derivatives of order 0 characterize continuity is studied. In particular, a measurable function satisfying EZI1if(x + fih) _ 0 must be a po...