Shamarova, E. Yu. Shamarov, N. N.
Published in
Russian Mathematics

In this paper we prove a variant of the Stokes formula for differential forms of a finite codimension in a locally convex space (LCS). The main tool used by us for proving the mentioned formula is the surface layer theorem for surfaces of codimension 1 in a locally convex space which was proved earlier by the first author. Moreover, on some subspac...

Papadopoulos, Athanase

This is the second edition of a book which appeared in 2005. The new edition is an expanded and revised version. The book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function is convex. We have also included a systematic introduction to the theory of geodesics and related matters i...

Gholizadeh, Leila Karapınar, Erdal Roohi, Mehdi
Published in
Fixed Point Theory and Applications

In this paper we investigate the existence of a fixed point of multivalued mapson almost p-convex and p-convex subsets of topological vectorspaces. Our results extend and generalize some fixed point theorems on the topicin the literature, such as the results of Himmelberg, Fan and Glicksberg. MSC: 46T99, 47H10, 54H25, 54E50, 55M20, 37C25.

Shatanawi, Wasfi Rajić, Vesna Ćojbašić Radenović, Stojan Al-Rawashdeh, Ahmed
Published in
Fixed Point Theory and Applications

In this paper, the concepts of a set-valued contraction of Mizoguchi-Takahashi type in the context of topological vector space (tvs)-cone metric spaces are introduced and a fixed point theorem in the context of tvs-cone metric spaces with respect to a solid cone is proved. We obtained results which extend and generalize the main results of S. H. Ch...

Latif, Abdul Hussain, Nawab Kutbi, Marwan A
Published in
Journal of Inequalities and Applications

In the setup of locally convex spaces, applying Caristi's results we prove some fixed point results for non-self multivalued maps and common fixed point theorems for Caristi type maps utilizing two different techniques. We apply our results to obtain some common fixed points for a Banach operator pair from the set of best approximations. Consequent...

Aksenov, N. A.
Published in
Mathematical Notes

We describe an analog of the Cauchy-Kovalevskaya sufficient conditions for the analytic solvability of the Cauchy problem for systems of operator-differential equations of arbitrary order in locally convex spaces; this analog is stated in terms of the order and type of the linear operator.

Aksyonov, N. A.
Published in
Russian Mathematics

In this paper we describe a method that allows one to study boundary-value problems for the first-order differential-operator equations in an arbitrary locally convex space.

Haluška, Ján Hutník, Ondrej
Published in
Mediterranean Journal of Mathematics

A Lebesgue-type integration theory in complete bornological locally convex topological vector spaces was introduced by the first author in [17]. In this paper we continue developing this integration technique and formulate and prove some theorems on integrable functions as well as some convergence theorems. An example of Dobrakov integral in non-me...

Kolesnikov, A. P.
Published in
Mathematical Notes

In the present paper, we propose a new approximation method in different function spaces. A specific feature of this method is that the choice of the basis approximating elements significantly depends on the topology of the given function space. Basis elements are constructed using the duality theory of locally convex spaces. A method of their exac...

Balaganskii, V. S.
Published in
Mathematical Notes