We provide some new results on the weak convergence of sequences or nets lying in L,((T, & r), X) = L,(p, X), 1 <p < co, i.e., the space of equivalence classes of X-valued (X is a Banach space) Bochner integrable functions on the finite measure space ( r, z, I”). Our theorems generalize in several directions recent resuls on weak sequential convergence in L,(p, X) obtained by M. A. Khan and M. ...

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

On $\mathscr{L}-$ fuzzy normed spaces, which is the generalization of notion lacunary statistical convergence for double sequences a convergence, are studied and developed in this paper. In addition, definitions Cauchy completeness related theorems given on spaces. Also, relationship Cauchyness boundedness with respect to norm shown.

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that  the category $L$-$mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.

This paper studies the equivalence of exponential ergodicity and L-exponential convergence mainly for continuous-time Markov chains. In the reversible case, we show that the known criteria for exponential ergodicity are also criteria for L-exponential convergence. Until now, no criterion for L-exponential convergence has appeared in the literature. Some estimates for the rate of convergence of ...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

In this paper we introduce strong $I^K$-convergence of functions which is common generalization of strong $I^*$-convergence of functions in probabilistic metric spaces. We also define and study strong $I^{K}$-limit points of functions in same space.