in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theore...

This paper focuses on the approximate controllability of Hilfer fractional neutral Volterra integro-differential inclusions via almost sectorial operators. Almost operators, differential, Leray-Schauder fixed point theorem and multivalued maps are used to prove result. We start by emphasizing existence a mild solution demonstrate system. In addition, an example is presented principle.

We study a nonlocal evolution equation generalising model introduced by Shigeru Kondo to explain colour patterns on skin of guppy fish. prove the existence stationary solutions using either bifurcation theory or Schauder fixed‐point theorem. also present numerical studies this and show that it exhibits similar those modelled well‐known reaction‐diffusion equations.

In this study, the existence and uniqueness of weak solution a coupled diffusion system is presented. Since considered problem nonlinear, first we consider corresponding linearized then use convergence method with Schauder fixed-point theorem to prove underlying in an appropriate Hilbert space. Moreover, computational experiments show that model could be applied image restoration problems.

Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

Using Banach’s contractive principle and the Laray–Schauder fixed point theorem, we study uniqueness existence of solutions to a nonlinear two-term fractional integro-differential equation with boundary condition based on Babenko’s approach Mittag–Leffler function. The current work also corrects major errors in published paper dealing one-term differential equation. Furthermore, provide example...

Introduction/purpose: This paper illustrates the existence of a generic Green's function for boundary value problem arbitrary order that appears in many phenomena heat convection, e.g. atmosphere, oceans, and on Sun's surface. Methods: A fixed point theorem Leray-Schauder form has been used to establish problem. Results: The solution shown an Some practical examples are proposed. Conclusions: n.