We investigate the existence of continuous solutions on compact intervals of some nonlinear integral equations. The existence of such solutions is based on some well-known fixed point theorems in Banach spaces such as Schaefer fixed point theorem, Schauder fixed point theorem, and Leray-Schauder principle. A special interest is devoted to the study of nonlinear Volterra equations and to the num...

We prove a generalization of a measure theoretic fixed point theorem of Darbo in Banach spaces which includes some well-known fixed point theorems of Dhage and Sadovskii as special cases. A generalized nonlinear functional integral equation is studied via Dhage fixed point theorem for attractivity of the solutions on unbounded intervals of real line. Finally the validity of our hypotheses impos...

In this short note, we propose a fixed point theorem in the setting of Banach space without using Picard operator.

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feas...

for all x, y ∈ X . Then there exists a unique fixed point x0 ∈ X of T . This theorem, called the Banach contraction principle, is a forceful tool in nonlinear analysis. This principle has many applications and is extended by several authors: Caristi [2], Edelstein [5], Ekeland [6, 7], Meir and Keeler [14], Nadler [15], and others. These theorems are also extended; see [4, 9, 10, 13, 23, 25, 26,...

In this article, a generalization of a Kakutani-Fan fixed point theorem for multi-valued mappings in Banach spaces is proved under weaker upper semi-continuity condition and it is further applied to derive a generalized version of Krasnoselskii’s fixed point theorem and some nonlinear alternatives of Leray-Schauder type for multi-valued closed mappings in Banach spaces. RESUMEN En este artículo...

for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

Introduction. We wish to summarize here some new asymptotic fixed point theorems. By an asymptotic fixed point theorem we mean roughly a theorem in functional analysis in which the existence of fixed points of a map ƒ is proved with the aid of assumptions on the iterates f of ƒ. Such theorems have proved of use in the theory of ordinary and functional differential equations (see [7], [8], [9] a...