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38 papers found.
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\(F(\psi,\varphi)\) -Contractions for α-admissible mappings on M-metric spaces

In this paper, we introduce certain α-admissible mappings which are \(F(\psi,\varphi)\)-contractions on M-metric spaces, and we establish some fixed point results. Our results generalize and extend some well-known results on this topic in the literature.

Positive Solutions for a System of Semipositone Fractional Difference Boundary Value Problems

Using the fixed point index, we establish two existence theorems for positive solutions to a system of semipositone fractional difference boundary value problems. We adopt nonnegative concave functions and nonnegative matrices to characterize the coupling behavior of our nonlinear terms.

Coincidence theory for compact morphisms

In this paper we present several coincidence type results for morphisms (fractions) in the sense of Gorniewicz and Granas.

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...

Compactness criteria and new impulsive functional dynamic equations on time scales

In this paper, we introduce the concept of Δ-sub-derivative on time scales to define ε-equivalent impulsive functional dynamic equations on almost periodic time scales. To obtain the existence of solutions for this type of dynamic equation, we establish some new theorems to characterize the compact sets in regulated function space on noncompact intervals of time scales. Also, by...

Lyapunov-type inequalities for a class of fractional differential equations

In this paper, we establish new Lyapunov-type inequalities for a class of fractional boundary value problems. As an application, we obtain a lower bound for the eigenvalues of corresponding equations. MSC: 26D10, 34A08, 34B09.

Lyapunov functions and strict stability of Caputo fractional differential equations

One of the main properties studied in the qualitative theory of differential equations is the stability of solutions. The stability of fractional order systems is quite recent. There are several approaches in the literature to study stability, one of which is the Lyapunov approach. However, the Lyapunov approach to fractional differential equations causes many difficulties. In...

Some generalizations of Darbo’s theorem and applications to fractional integral equations

In this paper, some generalizations of Darbo’s fixed point theorem are presented. An existence result for a class of fractional integral equations is given as an application of the obtained results.

On the existence of fixed points that belong to the zero set of a certain function

Let \(T: X\to X\) be a given operator and \(F_{T}\) be the set of its fixed points. For a certain function \(\varphi: X\to[0,\infty)\), we say that \(F_{T}\) is φ-admissible if \(F_{T}\) is nonempty and \(F_{T}\subseteq Z_{\varphi}\), where \(Z_{\varphi}\) is the zero set of φ. In this paper, we study the φ-admissibility of a new class of operators. As applications, we establish...

Structure of the solution set for a partial differential inclusion

In this paper, we consider the biharmonic problem of a partial differential inclusion with Dirichlet boundary conditions. We prove existence theorems for related partial differential inclusions with convex and nonconvex multivalued perturbations, and obtain an existence theorem on extremal solutions, and a strong relaxation theorem. Also we prove that the solution set is compact...

Fixed points of conditionally F-contractions in complete metric-like spaces

In this paper, we introduce the notion of a conditionally F-contraction in the setting of complete metric-like spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature.

Multi- C ∗ -ternary algebras and applications

In this paper, we look at the concept of multi- C ∗ -ternary algebras and consider some properties. As an application we approximate multi- C ∗ -ternary algebra homomorphisms and derivations in these spaces. MSC: 39A10, 39B72, 47H10, 46B03.

Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.

Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems

We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem.

Refinements of Generalized Hölder’s Inequalities

We present some new versions of generalized Hölder’s inequalities. The results are used to improve Minkowski’s inequality and a Beckenbach-type inequality.

Refinements of Generalized Hölder’s Inequalities

We present some new versions of generalized Hölder’s inequalities. The results are used to improve Minkowski’s inequality and a Beckenbach-type inequality.

Refinements of Generalized Hölder’s Inequalities

We present some new versions of generalized Hölder’s inequalities. The results are used to improve Minkowski’s inequality and a Beckenbach-type inequality.

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1):59-73, 2015; Adv. Differ. Equ. 2013:302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces.

Fixed points of generalized contractive mappings of integral type

The aim of this paper is to introduce classes of α-admissible generalized contractive type mappings of integral type and to discuss the existence of fixed points for these mappings in complete metric spaces. Our results improve and generalize fixed point results in the literature. MSC:46T99, 54H25, 47H10, 54E50.

Multiplicity and uniqueness results for the singular nonlocal boundary value problem involving nonlinear integral conditions

In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundary value problems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign.