Mohamed Jleli

Remarks on G-metric spaces and fixed point theorems

We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasi-metric spaces.MSC:47H10, 11J83.

A new generalization of the Banach contraction principle

We present a new generalization of the Banach contraction principle in the setting of Branciari metric spaces.

Best Proximity Points for Generalized α-ψ-Proximal Contractive Type Mappings.

We introduce a new class of non-self-contractive mappings. For such mappings, we study the existence and uniqueness of best proximity points. Several applications and interesting consequences of our obtained results are derived.

Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications

We derive some new coupled fixed point theorems for nonlinear contractive maps that satisfied a generalized Mizoguchi-Takahashis condition in the setting of ordered metric spaces. Presented theorems extends and generalize many well-known results in the literature. As an application, we give an existence and uniqueness theorem for the solution to a two-point boundary value problem.2000 Mathematics Subject Classification: 54H25; 47H10.

Lyapunov-type inequalities for fractional partial differential equations

Abstract We present Lyapunov inequalities for the fractional p-Laplacian ( − Δ p ) s , 1 p ∞ , s ∈ ( 0 , 1 ) , in an open bounded set Ω ⊂ R N , under homogeneous Dirichlet boundary conditions. We discuss two cases, the case s p > N and the case s p N . We use the obtained inequalities to provide lower bounds for the first eigenvalue of the fractional p-Laplacian. To the best of our knowledge, this is the first work dealing with Lyapunov-type inequalities for fractional partial differential equations.

Fixed Point Results for Almost Generalized Cyclic -Weak Contractive Type Mappings with Applications

We define a class of almost generalized cyclic -weak contractive mappings and discuss the existence and uniqueness of fixed points for such mappings. We present some examples to illustrate our results. Moreover, we state some applications of our main results in nonlinear integral equations.

Fixed Point Results for --Contractions on Gauge Spaces and Applications

We extend the concept of α-ψ-contractive mappings introduced recently by Samet et al. (2012) to the setting of gauge spaces. New fixed point results are established on such spaces, and some applications to nonlinear integral equations on the half-line are presented.

A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition

We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real zeros.

Further Remarks on Fixed-Point Theorems in the Context of Partial Metric Spaces

New fixed-point theorems on metric spaces are established, and analogous results on partial metric spaces are deduced. This work can be considered as a continuation of the paper Samet et al. (2013).

Best Proximity Points for Generalized -Proximal Contractive Type Mappings

We introduce a new class of non-self-contractive mappings. For such mappings, we study the existence and uniqueness of best proximity points. Several applications and interesting consequences of our obtained results are derived.