Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GET...Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.展开更多
The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics BY combining new principles of virtual velocity and virtual angular velocity as well...The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics BY combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress anti virtual couple stress with c ross terms of incremental rate type a new principle of power anti energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.展开更多
In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator...In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.展开更多
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t...The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.展开更多
In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is ...In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.展开更多
In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-...In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.展开更多
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity s...In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.展开更多
In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an exist...In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.展开更多
The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the...The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.展开更多
文摘Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.
文摘The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics BY combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress anti virtual couple stress with c ross terms of incremental rate type a new principle of power anti energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.
文摘In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.
文摘The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.
文摘In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.
基金supported by the Natural Science Foundation of Sichuan Education Department of China(No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
基金This project is supported by Natural Science Foundation of Sichuan Education Department of China(2003A081)SZD0406
文摘In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.
基金Supported by the National Natural Science Foundation of China (No. 10771058)the Hunan Provincial Natural Science Foundation (No. 09JJ6013)
文摘In this paper, we establish some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces. As applications, some minimax inequalities and an existence theorem of equilibrium points for an abstract generalized vector equilibrium problem are proved in topological spaces. The results presented in this paper unify and generalize some known results in recent literature.
文摘The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.
