Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2011
Volume
Vol. 31
Number
No. 1
Description
Journal Volume
Opuscula Mathematica
Vol. 31 (2011)
Projects
Pages
Articles
A Meir-Keeler type common fixed point theorem for four mappings
(2011) Akkouchi, Mohamed
In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result generalizes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly compatibility property and replacing the completeness of the space with a set of four alternative conditions for maps satisfying an implicit relation. Also, our result improves the main result of H. Bouhadjera, A. Djoudi.
On strongly midconvex functions
(2011) Azócar, A.; Giménez, J.; Nikodem, K.; Sánchez, J. L.
In this paper we collect some properties of strongly midconvex functions. First, counterparts of the classical theorems of Bernstein-Doetsch, Ostrowski and Sierpiński are presented. A version of Rod é support theorem for strongly midconvex functions and a Kuhn-type result on the relation between strongly midconvex functions and strongly $t$-convex functions are obtained. Finally, a connection between strong midconvexity and generalized convexity in the sense of Beckenbach is established.
Multi-valued codensing random operators and functional random integral inclusions
(2011) Dhage, Bapurao C.
In this paper, some random fixed point theorems for continuous and condensing multi-valued random operators are proved and they are further applied to the random integral inclusions for proving the existence of the solutions via the priori bound method.
On operators of transition in Krein spaces
(2011) Grod, A.; Kuzhel, S.; Sudilovskaya, V.
The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix $L$. In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455–486) and show the equivalence between the existence of a strong solution $K$ ($\|K\|\lt 1$) of the Riccati equation and similarity of the $J$-self-adjoint operator $L$ to a self-adjoint one.
Existence and uniqueness of anti-periodic solutions for a class of nonlinear n-th order functional differential equations
(2011) Liu, Ling; Li, Yongkun
In this paper, we use the method of coincide degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear n-th order functional differential equations of the form $x^{(n)}(t)=F(t, x_t, x^{(n-1)}_t, x(t), x^{(n-1)}(t), x(t-\tau(t)), x^{(n-1)}(t-\sigma(t))).$