In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point t...In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.展开更多
Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems co...Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.展开更多
本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间...本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.展开更多
In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） i...In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.展开更多
By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous ...By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .展开更多
文摘In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.
文摘Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.
文摘本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.
文摘In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Uiam-Rassias stability of the functional equation 6f（x＋y）-6f（x-y）＋4f（3y）=3f（x＋2y）-3f（x-2y）＋9f（2y） in fuzzy Banach spaces. We can find the range of approximate solutions obtained using the direct method are less than those obtained by using the fixed point alternative method for the above and the functional equation.
文摘By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative .
