4 The Dwork-Robba theorem and the upper semicontinuity of ξ 7→ R(ξ,Σ) 9 4.1 The global growth estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.2 The generalized Dwork-Robba theorem . . . . . . . . . . . . . . . . . . . . . . 10 4.3 Upper semicontinuity of ξ 7→ R(ξ,Σ) . . . . . . . . . . . . . . . . . . . . . . . 13 4.4 Continuity of ξ 7→ R(ξ,Σ) at maximal points (Dwork’s tra...

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a TVS-valued cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.

We introduce a new notion called weakly contra-(μ, λ)-continuous functions as functions on generalized topological spaces [17]. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of weak contra-continuity due to Baker [9]. Mathematics Subject Classification (2010): 54A05, 54C10.

We discuss a differential equations treatment of the implicit functions problem. Our approach allows a precise and complete description of the solution, of continuity and differentiability properties. The critical case is also considered. The investigation is devoted to dimension two and three, but extensions to higher dimension are possible. MSC: 26B10, 34A12, 53A05. keywords: implicit functio...

The results presented in this paper extend and complement the corresponding ones of Hussain-Jungck[Common fixed point and invariant approximation results for noncommuting generalized (f,g)-nonexpansive maps, J. Math. Anal. Appl. 321(2006), 851-861], and drop some restricts such as the continuity of f, g and demiclsedness of f − T . Mathematics Subject Classification: 41A50, 47H10, 54H25

We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (depending on a constant which may be different from the standard quantum constant h̄) is equivalent to a generalized Schrödinger equation for a ‘wavefunction’ whose modulus squared yields the fluid density. Then we show th...

An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations with the structure 0 ∈ F(z) + T (z), where T is a multifunction and F is singlevalued, the framework covers methods that, at each step, solve subproblems of the type 0 ∈ A(z, s)+ T (z). The multifunction A approximates F around s. Besides a condition on the quality of this...

We introduce new clustering coefficients for weighted networks. They are continuous and robust against edge weight changes. Recently, generalized clustering coefficients for weighted and directed networks have been proposed. These generalizations have a common property, that their values are not continuous. They are sensitive with edge weight changes, especially at zero weight. With these gener...