[PDF] Top 20 Fixed point theorems with applications to n-th order ordinary differential equations

... extend fixed point of weak contractions to cone metric ...and ordinary differential equations could be sourced from ( [15], [3], [13], [9], ... See full document

... hybrid fixed point theorems of Krasnosel’skii type and some nonlinear alternatives of Leray-Schauder type involving sums of two operators in a partially ordered normed linear ...integral ... See full document

... he fixed point theorems concern maps f of a set X into itself that, under certain conditions, admit a fixed point, that is, a point x ∈ X such that f(x) = ...of fixed ... See full document

... the fixed point has important applications in fields such as differential equations, equilibrium pro- blems, variational inequality, optimization problems, maxmin problems ...of ... See full document

... [4] C.Z. Bai, J.X. Fang: The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Applied Mathematics and Computation, Vol. 150, Iss. 3, pp. ... See full document

... fixed point theorem for se- quentially weakly continuous mappings has been proved in ...fixed point theorem allowed, in many applications, to avoid some contractiveness conditions generated by the use ... See full document

... ( ' ) k ∈ L 1 (α, β)). Then there exists a unique solution x ∈ C 1 (I,X) to the Cauchy problem 3.2, for every I ⊂ (α, β). proof :Proceed like in the proof of Theorem 3.3, taking now Z = C(I,X).When f is merely continuous ... See full document

... the fixed point theory yields result of best approximation and best approxi- mation yields the variational inequality ...yields fixed point theory. It is also shown that the fixed ... See full document

... By setting px, y px in Theorem 3.5, we have the following: COROLLARY :}.6 Let X,.T’ be a probabilistic quasi-metric space and let S and T be two commuting self-mappings of X.. If these c[r] ... See full document

... Theorem 1.1 (Banach [7]) Let (X, d) be a complete metric space and let T : X ® X be a contraction, i.e., there exists k Î [0, 1) such that d(Tx, Ty) ≤ kd(x, y) for all x, y Î X. Then T has a unique fixed ... See full document

... Remark . In Theorem ., Theorem ., Corollary . and Corollary . above, we al- ways assume that T is upper -preserving and f ( · , y) is order-reversing for each y ∈ C and f (x, · ) is ... See full document

... fixed point theorems in a partially ordered -orbitally complete normed linear ...fixed point theorem, a coupled fixed point theorem for the mapping is ...As applications, we apply the ... See full document

... [, +∞) are continuous functions, in the general case, unbounded, and q : [, +∞) → R, f : [, +∞) × R → R are continuous functions. Note that, since the deviations are un- bounded, we cannot apply the well-known fixed ... See full document

... coincidence point has been studied in [–] and the references ...fixed point has been studied in [–] and the refer- ences ...coincidence point and common fixed point theorems in the ... See full document

... integral equations, (b) boundary value problems for semilinear ordinary differential equations, (c) boundary value problems for semilinear elliptic differential equations, (d) initial-value ... See full document

... partial order and discussed some applications to matrix ...fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric ... See full document

... Fixed point theory has fascinated applications with the evaluation of the Banach Contrac- tion ...Moreover, fixed point theory provides very important tools for providing the existence ... See full document

... Fixed point theorems for contractive operators in metric spaces are widely investigated and have found various applications in differential and integral equations (see [, , , ] ... See full document

... In this section we discuss the application of our results to the existence of solutions for Caputo fractional boundary value problem of order β ∈ (1, 2] with integral boundary con- dition type. As the definition of ... See full document

... Banach fixed point Theorem and the nonlinear alternative of Leray–Schauder principle to investigate the existence of solutions for fractional order functional and neutral functional ... See full document