Sentence examples for modular spaces in from inspiring English sources

Visitors will be allowed to enter the interiors of the modular spaces in small groups.

In 1950 Nakano [1] introduced the theory of modular spaces in connection with the theory of ordered spaces.

Razani et al. studied the fixed points of nonlinear and asymptotic contractions in the modular space in 2007.

In this paper, we introduce the notions of nonlinear contractions in modular spaces and establish their fixed points theorems in modular spaces.

In addition, quasi-contraction mappings in modular spaces without Δ 2 -condition were considered by Khamsi [6] in 2008.

Fixed point theorems in modular spaces, generalizing the classical Banach fixed point theorem in metric spaces, have been studied extensively.

Even though a metric is not defined, many problems in fixed point theory can be reformulated in modular spaces (see [15 20] and references therein).

Even though a metric is not defined, many problems in metric fixed point theory can be reformulated in modular spaces.

Even though a metric is not defined, many problems in metric fixed point theory can be reformulated and solved in modular spaces (see, for instance, [36 39]).

Using the idea of Pata, we prove a fixed point theorem in modular spaces.

Recently, we proved the fixed points of asymptotic pointwise nonexpansive mappings in modular spaces [8].