1,721,060 research outputs found
Comments on the paper "COINCIDENCE THEOREMS FOR SOME MULTIVALUED MAPPINGS" by B. E. RHOADES, S. L. SINGH AND CHITRA KULSHRESTHA
Full text linkThe aim of this note is to point out an error in the proof of Theorem 1 in the paper entitled “Coincidence theorems for some multivalued mappings” by B. E. Rhoades, S. L. Singh and Chitra Kulshrestha [Internat. J. Math. & Math. Sci., 7 (1984), 429-434], and to indicate a way to repair it
Coupled fixed point, F-invariant set and fixed point of N-order
No full textIn this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of -invariant set. We introduce the notion of fixed point of -order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature
On semilinear inequalities involving the Dunkl Laplacian and an inverse-square potential outside a ball
Full text linkLet Delta kbe the Dunkl generalized Laplacian operator associated with a root systemRofN,>= N2, anda nonnegative multiplicity functionkdefined onRand invariant by thefinite reflection groupW. In this study,we study the existence and nonexistence of weak solutions to the semilinear inequality-+>=Delta uu uk lambda xp2 divided by divided by divided by divided by inB\N1under the boundary condition >= u0on partial derivative B1, where>p1,>=-- +/lambda N gamma 22 42(), andB1is the open unitball ofN. Namely, we show that the dividing line with respect to existence and nonexistence is given by acritical exponent that depends on lambda,N, and gamma k(), where=& sum;is an element of+gamma kk alpha alpha R()()and+Ris the positive subsystem
Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces
No full textIn this paper, we establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to Ciric (2009) [3]. An example is given to illustrate the usability of our results
From metric spaces to partial metric spaces
Full text linkMotivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced
Liouville-type results for semilinear inequalities involving the Dunkl Laplacian operator
No full textLet Delta_k be the Dunkl generalized Laplacian operator associated to a root system R of R^N and a nonnegative multiplicity function k defined on R and invariant by the finite reflection group W. In this paper, we establish Liouville-type theorems for the semilinear inequality -Delta_k u >= |u|(p )in R-N and the system of inequalities -Delta_k u >= |v|(p), -Delta_k v >= |u|(q )in R^N, where N >= 1 and p, q >1. To the best of our knowledge, this contribution is the first work dealing with Liouville-type results for nonlinear problems involving the Dunkl Laplacian
A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space
No full textRecently, Azam, Arshad and Beg [4] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result
Nonexistence results for higher order fractional differential inequalities with nonlinearities involving Caputo fractional derivative
Full text linkHigher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function
On the critical curve for systems of hyperbolic inequalities in an exterior domain of the half-space
Full text linkWe establish blow-up results for a system of semilinear hyperbolic inequalities in an exterior domain of the half-space. The considered system is investigated under an inhomogeneous Dirichlet-type boundary condition depending on both time and space variables. In certain cases, an optimal criterium of Fujita-type is derived. Our results yield naturally sharp nonexistence criteria for the corresponding stationary wave system and equation
Higher order evolution inequalities involving Leray-Hardy potential singular on the boundary
Full text linkWe consider a higher order (in time) evolution inequality posed in the half ball, under Dirichlet type boundary conditions. The involved elliptic operator is the sum of a Laplace differential operator and a Leray-Hardy potential with a singularity located at the boundary. Using a unified approach, we establish a sharp nonexistence result for the evolution inequalities and hence for the corresponding elliptic inequalities. We also investigate the influence of a nonlinear memory term on the existence of solutions to the Dirichlet problem, without imposing any restrictions on the sign of solutions
- …
