1,721,161 research outputs found
The class of F-contraction mappings with a measure of noncompactness
No full textIn this chapter we review a class of contraction conditions, which are largely used to obtain interesting generalizations of the Banach fixed-point theorem in various abstract settings. We also present a new fixed-point existence result obtained by considering such a kind of contraction condition and a measure of noncompactness. Moreover, we show the applicability of these results in the theory of functional equations
Fixed point iterative schemes for variational inequality problems
No full textWe apply fixed point iterative schemes to variational inequality problems, via admissible perturbations of projection operators in real Hilbert spaces. Then, we prove some convergence theorems, extending and complementing the results in the existing literature. In particular, we deal with the class of α-co-coercive operators with application to general equilibrium problems
A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators
No full textWe consider relatively Meir-Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. ['Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness', Acta Math. Sci. Ser. B 35 (2015), 552-566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations
A note on best proximity point theory using proximal contractions
No full textIn this paper, a reduction technique is used to show that some recent results on the existence of best proximity points for various classes of proximal contractions can be concluded from the corresponding results in fixed point theory
Multiple solutions for (p,2)-equations at resonance
Full text linkWe consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them
A New Approach to the Generalization of Darbo’s Fixed Point Problem by Using Simulation Functions with Application to Integral Equations
Full text linkWe investigate the existence of fixed points of self-mappings via simulation functions and measure of noncompactness. We use different classes of additional functions to get some general contractive inequalities. As an application of our main conclusions, we survey the existence of a solution for a class of integral equations under some new conditions. An example will be given to support our results
Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations
Full text linkWe consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations
Superlinear Robin Problems with Indefinite Linear Part
Full text linkWe consider a semilinear Robin problem with an indefinite linear part and a superlinear reaction term, which does not satisfy the usual in such cases AR condition. Using variational methods, together with truncation–perturbation techniques and Morse theory (critical groups), we establish the existence of three nontrivial solutions. Our result extends in different ways the multiplicity theorem of Wang
Fixed point results under generalized c-distance with application to nonlinear fourth-order differential equation
Full text linkWe consider the notion of generalized c-distance in the setting of ordered cone b-metric spaces and obtain some new fixed point results. Our results provide a more general statement, under which can be unified some theorems of the existing literature. In particular, we refer to the results of Sintunavarat et al. [W. Sintunavarat, Y.J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. 62 (2011) 1969-1978]. Some examples and an application to nonlinear fourth-order differential equation are given to support the theory
Parametric nonlinear singular Dirichlet problems
Full text linkWe consider a nonlinear parametric Dirichlet problem driven by the p-Laplacian and a reaction which exhibits the competing effects of a singular term and of a resonant perturbation. Using variational methods together with suitable truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence on the parameter of the set of positive solutions
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