For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

Weakly harmonic maps from a domain Ω⊂Rd, d≥2 (the upper half-space R+d or bounded C1,α domain, α∈(0,1]) into smooth closed manifold are studied. Prescribing small Dirichlet data in either of the classes L∞(∂Ω) BMO(∂Ω), we establish solvability resulting boundary value problems by means nonvariational method. As by-product, solutions shown to be locally smooth, Cloc∞. Moreover, show that can cho...

Introduction Sessa [9] generalized the notion of commuting maps given by Jungck [2] and introduced weakly commuting mappings. Further, Jungck [3] introduced more generalized commutativity called compatibility. In 1998, Jungck and Rhoades [4] introduced the notion of weakly compatible maps and showed that compatible maps are weakly compatible but converse need not true. Menger [5] introduced the...

In this paper, we prove common fixed point theorems for a pair of weakly compatible maps under E.A .property. A major benefit of property (E.A.) is that it ensures convergence of desired sequences without completeness. At the end we rectify the main result of the paper, entitled “Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 111(2001), No. 2, pp 241-247.

We review the basic steps leading to the construction of a Sinai-Ruelle-Bowen (SRB) measure for an innnite lattice of weakly coupled expanding circle maps, and we show that this measure has exponential decay of space-time correlations. First, using the Perron-Frobenius operator, one connects the dynamical system of coupled maps on a d-dimensional lattice to an equilibrium statistical mechanical...

In this paper we introduce the concept of semi weakly compatibility of maps and establish some common fixed point theorems by using this concept along with the notion of weakly compatibility of maps in the setting of non-complete intuitionistic fuzzy metric spaces. Our results extend and generalize the result of Pant et al [18]. Some related results and illustrative examples have also been disc...