Ariana Pitea

Some coupled fixed point theorems in quasi-partial metric spaces

In this paper, we study some coupled fixed point results in a quasi-partial metric space. Also, we introduce some examples to support the useability of our results.MSC:47H10, 54H25.

Duality theorems for a new class of multitime multiobjective variational problems

In this work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (ρ, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature.

Contraction conditions using comparison functions on b-metric spaces

AbstractIn this paper, we consider the setting of b-metric spaces to establish results regarding the common fixed points of two mappings, using a contraction condition defined by means of a comparison function. An example is presented to support our results comparing with existing ones. MSC:49H09, 47H10.

Minimization of vectors of curvilinear functionals on the second order jet bundle

Consider the multi-time multi-objective variational problem (MFP) of minimizing a vector of quotients of path independent curvilinear functionals subject to PDE and/or PDI constraints. The goal of our work is to develop an optimization theory for the second order jet bundle. While the background in Sect. 1 is introductory, the theory in Sects. 2 and 3 is new as a whole, containing our results.

Fixed and coupled fixed point theorems of omega-distance for nonlinear contraction

In this paper we utilize the notion of Ω-distance in the sense of Saadati et al. (Math. Comput. Model. 52:797-801, 2010) to construct and prove some fixed and coupled fixed point theorems in a complete G-metric space for a nonlinear contraction. Also, we provide an example to support our results.MSC:47H10, 54H25.

Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions

Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011)), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.

Ω-Distance and coupled fixed point in G-metric spaces

Saadati et al. (Math. Comput. Model. 52:797-801, 2010) introduced the concept of Ω-distance in generalized metric spaces and studied some nice fixed point theorems. Very recently, Jleli and Samet (Fixed Point Theory Appl. 2012:210, 2012) showed that some of the fixed point theorems in G-metric spaces can be obtained from quasi-metric space. In this paper, we utilize the concept of Ω-distance in the sense of Saadati et al. to establish some common coupled fixed point results. Also, we introduce an example to support the useability of our results. Note that the method of Jleli and Samet cannot be used in our results.MSC:47H10, 54H25.

Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems

In this paper, a new class of generalized of nonconvex multitime multiobjective variational problems is considered. We prove the sufficient optimality conditions for efficiency and proper efficiency in the considered multitime multiobjective variational problems with univex functionals. Further, for such vector variational problems, various duality results in the sense of Mond-Weir and in the sense of Wolfe are established under univexity. The results established in the paper extend and generalize results existing in the literature for such vector variational problems.MSC:65K10, 90C29, 90C30.

A GEOMETRIC STUDY OF SOME EQUATIONS OF MATHEMATICAL PHYSICS

We introduce geometric structures (connections, pseudo-Riemannian metrics) adapted to some fundamental problems of Differential Geometry, and find geometrical characteristics associated to equations of Mathematical Physics. Also, we introduce a geometric study of some boundary problems. Throughout this work, as main tool we employed an adequate Riemannian Hessian structure, suggested in [Int. J. Geom. Meth. Mod. Phys.7(7) (2010) 1104–1113].

ON NEW CLASSES OF EXPLICIT QUASI-EINSTEIN RIEMANNIAN MANIFOLDS

This paper aims to introduce new classes of two-dimensional quasi-Einstein Riemannian manifolds, endowed with generalized Poincare metrics.