In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. The fully discrete, fully second order finite difference scheme in question was derived in a re...

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

banach contraction principle has been generalized in different spaces by mathematicians over the years. mustafa and sims [18] proposed a new class of generalized metric spaces, which are called as g-metric spaces. in this type of spaces a non-negative real number is assigned to every triplet of elements. many mathematicians studied extensively various results on g-metric spaces by using the con...

In this paper, we first introduce a class of nonlinear mappings called extended hybrid in a Hilbert space containing the class of generalized hybrid mappings. The class is different from the class of super hybrid mappings which was defined by Kocourek, Takahashi and Yao [12]. We prove a fixed point theorem for generalized hybrid nonself-mapping in a Hilbert space. Next, we prove a nonlinear erg...

the concept of ${mathscr{f}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{f}}$. its equivalence to the concept of ${mathscr{f}}$-convergence in uniform spaces is proved. this convergence generalizes many kinds of convergence, including the well-known statistical convergence.

in this study, 2n -dimensional (n > 2) generalized conformally recurrent kaehlerian weyl spaces andgeneralized conharmonicaly recurrent kaehlerian weyl spaces are defined. it is proved that a kaehlerian weylspace is generalized conformally recurrent if and only if it is generalized recurrent.also, it is shown that akaehlerian weyl space will be generalized recurrent if and only if it is general...

Let C be a nonempty closed and convex subset of a real Hilbert space H. Let Am, Bm : C → H be relaxed cocoercive mappings for each 1 ≤ m ≤ r, where r ≥ 1 is integer. Let f : C → C be a contraction with coefficient k ∈ (0, 1). Let G : C → C be ξ-strongly monotone and L-Lipschitz continuous mappings. Under the assumption ∩m=1GV I(C,Bm, Am) 6= ∅, where GV I(C,Bm, Am) is the solution set of a gener...

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

Some fixed point convergence properties are proved for compact and demicompact maps acting over closed, bounded and convex subsets of a real Hilbert space. We also show that for a generalized nonexpansive mapping in a uniformly convex Banach space the Ishikawa iterates converge to a fixed point. Finally, a convergence type result is established for multivalued contractive mappings acting on clo...