In this paper, we prove a fixed point theorem for a pair of generalized weakly contractive mappings in complete partial metric spaces. The theorems presented are generalizations of very recent fixed point theorems due to Abdeljawad, Karapinar and Tas. To emphasize the very general nature of these results, we illustrate an example.

This paper is concerned with proving the existence of solutions to an underdetermined system of equations and with the application to existence of spherical t-designs with (t+ 1)2 points on the unit sphere S2 in R3. We show that the construction of spherical designs is equivalent to solution of underdetermined equations. A new verification method for underdetermined equations is derived using B...

The expression and properties of Green’s function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind. The r...

In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem D0+u(t) = f(t, u(t)), 0 < t < 1 u(0) + u′(0) = 0, u(1) + u′(1) = 0 where 1 < α ≤ 2 is a real number, and D0+ is the Caputo’s fractional derivative, and f : [0, 1]×[0,+∞)→ [0,+∞) is continuous. By means of a fixed-point theorem on cones, some e...

In this work, we investigate the eigenvalue intervals of nonlinear boundary value problems involving fractional q -difference equations by means of the properties of the Green function and Guo-Krasnosel’skii fixed point theorem on cones. Furthermore, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are establi...

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.

Copyright q 2010 Jing Xiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper uses a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order impulsive...

This paper is devoted to studying some new existence theorems for single and multiple positive periodic solutions to a scalar functional differential equation by combining some properties of Green’s function together with a well-known nonzero fixed point theorem in cones. It improves and generalizes some related results in the literature. Finally, several examples and numerical simulations are ...

where 1 < α < 2, 0 < βi < 1, i = 1, 2, . . . ,m – 2, 0 < η1 < η2 < · · · < ηm–2 < 1, ∑m–2 i=1 βiη α–1 i < 1, D α 0+ is the standard Riemann–Liouville derivative. Here our nonlinearity f may be singular at u = 0. As an application of Green’s function, we give some multiple positive solutions for singular positone and semipositone boundary value problems by means of the Leray–Schauder nonlinear a...

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...