An extension of Darbo's theorem and its application to system of neutral differential equations with deviating argument

Abstract

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations.

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

“…Then, there exists y ∈ Z such that f (y) ≤ f (x); d(x, y) ≤ 1 and f (z) > f (y) − d(y, z) for all y = z. Now, we study generalized metric spaces and their properties, for more details and application, we refer to [7,[14][15][16][17][18][19][20][21][22][23].…”

Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument

“…The IONLDE with advanced arguments have frequently been used by the researches associated to the field of mathematical physics, mechanical engineering and economics, for instance read the monographs of Agarwal et al [3], Burton [10], and Jankowski [23,25]. More about on the practical uses of IONLDE with advanced argument could be found in Augustynowicz et al [7], Banaei et al [9], El-Sayed [18], Jankowski [26], and Yang et al [40]. From the applicable point of view, FONLDE with advanced argument is more significant than IONLDE with advanced argument.…”

Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

“…For more details on the theory of measure of noncompactness, its applications and its relations with nonlinear analysis we refer the reader to [8][9][10][11][12][13].…”