We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth ad...We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.展开更多
In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contracti...In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.展开更多
Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the...Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.展开更多
A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condit...A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.展开更多
The purpose of this note is to set up a unified theory on scalar, electromagnetic and gravitational field. By resolving the 5-dimensions of Riemann manifold to (4+1)-dimensions, we first define the Lagrangian density,...The purpose of this note is to set up a unified theory on scalar, electromagnetic and gravitational field. By resolving the 5-dimensions of Riemann manifold to (4+1)-dimensions, we first define the Lagrangian density, so as to set up a new field equation, and then discuss some properties of the unified field.展开更多
文摘We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.
文摘In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.
文摘Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.
基金supported by the National Natural Science Foundation of China(No.11361064)
文摘A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.
文摘The purpose of this note is to set up a unified theory on scalar, electromagnetic and gravitational field. By resolving the 5-dimensions of Riemann manifold to (4+1)-dimensions, we first define the Lagrangian density, so as to set up a new field equation, and then discuss some properties of the unified field.
