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Fixed point theory for Mönch-type maps defined on closed subsets of Fréchet spaces: the projective limit approach

Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences RAVI P. AGARWAL JEWGENI H. DSHALALOW DONAL O'REGAN New Leray-Schauder alternatives are presented for Mo ... ( 2000 ), no. 2 , 594 - 612 . Ravi P. Agarwal: Department of Mathematical Sciences, College of Science, Florida Institute of Technology, Melbourne, FL 32901 -6975, USA E-mail address: Jewgeni H. Dshalalow

A note on Ćirić type nonunique fixed point theorems

In this paper, we suggest some nonunique fixed results in the setting of various abstract spaces. The proposed results extend, generalize and unify many existing results in the corresponding literature.

Fractional-order differential equations with anti-periodic boundary conditions: a survey

We will present an up-to-date review on anti-periodic boundary value problems of fractional-order differential equations and inclusions. Some recent and new results on nonlinear coupled fractional differential equations supplemented with coupled anti-periodic boundary conditions will also be highlighted.

Fractional-order differential equations with anti-periodic boundary conditions: a survey

We will present an up-to-date review on anti-periodic boundary value problems of fractional-order differential equations and inclusions. Some recent and new results on nonlinear coupled fractional differential equations supplemented with coupled anti-periodic boundary conditions will also be highlighted.

A matched space for time scales and applications to the study on functions

In this paper, using the algebraic structure of the Abelian group, we introduce the concept of a matched space for time scales, and we construct the algebraic structure of matched spaces to solve the closedness of time scales under non-translational shifts. Using a matched space for time scales, a new concept of periodic time scales is introduced. Based on it, new concepts of...

Proving uniqueness for the solution of the problem of homogeneous and anisotropic micropolar thermoelasticity

In this paper we derive some identities for the solution of the problem of homogeneous and anisotropic micropolar thermoelasticity. These can be applied to proving uniqueness of the solution of the corresponding boundary initial value problem.

Positive solutions of fractional integral equations by the technique of measure of noncompactness

Agarwal 2 Manuel De la Sen 0 0 Institute of Research and Development of Processes IIDP Faculty of Science and Technology, University of the Basque Country , Leioa , Spain 1 Department of Mathematics, Sari

Positive solutions of higher-order Sturm-Liouville boundary value problems with derivative-dependent nonlinear terms

We consider the Sturm-Liouville boundary value problem { y ( m ) ( t ) + F ( t , y ( t ) , y ′ ( t ) , … , y ( q ) ( t ) ) = 0 , t ∈ [ 0 , 1 ] , y ( k ) ( 0 ) = 0 , 0 ≤ k ≤ m − 3 , ζ y ( m − 2 ) ( 0 ) − θ y ( m − 1 ) ( 0 ) = 0 , ρ y ( m − 2 ) ( 1 ) + δ y ( m − 1 ) ( 1 ) = 0 , where m ≥ 3 and 1 ≤ q ≤ m − 2 . We note that the nonlinear term F involves derivatives. This makes the...

New applications of Calvert and Gupta’s results to hyperbolic differential equation with mixed boundaries

Calvert and Gupta’s results concerning the perturbations on the ranges of m-accretive mappings have been employed widely in the discussion of the existence of solutions of nonlinear elliptic differential equation with Neumann boundary. In this paper, we shall focus our attention on certain hyperbolic differential equation with mixed boundaries. By defining some suitable nonlinear...

Compactness criteria and new impulsive functional dynamic equations on time scales

P Agarwal 1 Donal O'Regan 0 0 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland , Galway , Ireland 1 Department of Mathematics, Texas A&M University-Kingsville

A new iterative algorithm for the sum of infinite m-accretive mappings and infinite \(\mu_{i}\) -inversely strongly accretive mappings and its applications to integro-differential systems

A new three-step iterative algorithm for approximating the zero point of the sum of an infinite family of m-accretive mappings and an infinite family of \(\mu_{i}\)-inversely strongly accretive mappings in a real q-uniformly smooth and uniformly convex Banach space is presented. The computational error in each step is being considered. A strong convergence theorem is proved by...

Iterative algorithms for infinite accretive mappings and applications to p-Laplacian-like differential systems

Some new iterative algorithms with errors for approximating common zero point of an infinite family of m-accretive mappings in a real Banach space are presented. A path convergence theorem and some new weak and strong convergence theorems are proved by means of some new techniques, which extend the corresponding works by some authors. As applications, an infinite p-Laplacian-like...

Nonconstant periodic solutions for a class of ordinary p-Laplacian systems

In this paper, we study the existence of periodic solutions for a class of ordinary p-Laplacian systems. Our technique is based on the generalized mountain pass theorem of Rabinowitz. MSC: 47J30, 34B15, 34C25, 35B38.

Existence results for sequential fractional integro-differential equations with nonlocal multi-point and strip conditions

In this paper we investigate a new kind of nonlocal multi-point boundary value problem of Caputo type sequential fractional integro-differential equations involving Riemann-Liouville integral boundary conditions. Several existence and uniqueness results are obtained via suitable fixed point theorems. Some illustrative examples are also presented. The paper concludes with some...

Relatively dense sets, corrected uniformly almost periodic functions on time scales, and generalizations

In this paper, we use the analysis of relatively dense sets to point out some deficiencies and inaccuracies in the definition of uniformly almost periodic functions which has been proposed in recent works, and we correct it. Some new generalizations of invariance under translation time scales and almost periodic functions are established. Our study will ensure that now we can...

Changing-periodic time scales and decomposition theorems of time scales with applications to functions with local almost periodicity and automorphy

Chao Wang Ravi P Agarwal In this work, we address the periodic coverage phenomenon on arbitrary unbounded time scales and initiate a new idea, namely, we introduce the concept of changing-periodic time

An essential remark on fixed point results on multiplicative metric spaces

In this short note, we announce that all the presented fixed point results in the setting of multiplicative metric spaces can be derived from the corresponding existing results in the context of standard metric spaces in the literature.

Fractional differential equations and inclusions with semiperiodic and three-point boundary conditions

In this article, we investigate the existence of solutions for boundary value problems of fractional differential equations and inclusions with semiperiodic and three-point boundary conditions. The existence results for equations are obtained by applying Banach’s contraction mapping principle, Schaefer-type fixed point theorem, Leray-Schauder degree theory, Krasnoselskii’s fixed...