In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usua...In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usual conditions in cone metric spaces.展开更多
The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M(x + d)}is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some s...The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M(x + d)}is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understanding the non-spectral and spectral of μM,D. As an application,we show that the L~2(μM,D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.展开更多
The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction con...The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces.It is noted that a metric can induce a multiplicative metric,and conversely,a multiplicative metric can give a rise to a metric on a nonempty set.As an application,another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.展开更多
基金Supported by the Fundamental Research Fund of Sichuan Provincial Science and Technology Department(2012JYZ019)
文摘In this paper, some new existence and uniqueness of points of coincidence of weakly compatible pair of mappings is obtained, which does not satisfy continuity and commutativity. The conditions are weaker than the usual conditions in cone metric spaces.
基金supported by National Natural Science Foundation of China(Grant No.11101334)
文摘The self-affine measure μM,Dassociated with an iterated function system{φd(x)=M(x + d)}is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understanding the non-spectral and spectral of μM,D. As an application,we show that the L~2(μM,D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.
基金Supported by the General Project of Science and Technology Department of Sichuan Province(2018JY0256)the Scientific Research Fund of Leshan Normal University(DGZZ202024)。
文摘The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces.It is noted that a metric can induce a multiplicative metric,and conversely,a multiplicative metric can give a rise to a metric on a nonempty set.As an application,another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.
