in this paper, we prove some approximate fixed point results for proximinal valued $beta$-contractive multifunctions on metric spaces. we show that our results generalize some old fixed point results in the literature.

in this paper, the notion of n, pn - summability to generalize the concept of statisticalconvergence is used. we call this new method weighted statistically convergence. we also establish itsrelationship with statistical convergence, c,1-summability and strong   n n, p -summability.

Based on the general form of -resolution principle for a lattice-valued logic with truth-values defined in a latticevalued logical algebra structure lattice implication algebra, the further extended -resolution method in this lattice-valued logic is discussed in the present paper in order to increase the efficiency of the resolution method. Firstly, -quasi-lock semantic resolution method in lat...

The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category CONV of convergence spaces. It is well known that the category DCPO of dcpos and Scott continuous functions can be embedded into TOP, and so into CONV, by considering the Scott topology. We propose a di3erent, “cotopological” embedding of DCPO into CONV, which, in contrast to t...

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is splitted into the sum of a single-valued operator F , possessing a kind of pseudo Dunn property, and a maximal monotone operator Q. The current auxiliary problem is constructed by fixing F at the...

CD0-type spaces were firstly introduced by Yu. A. Abramovich and A. W. Wickstead in [1] and [2] and further investigated by S. Alpay and Z. Ercan in [3]. CD0-type spaces deserve to be called Abramovich–Wickstead spaces, or briefly AW -space as in [4], since they mainly stem from the works of Yu. A. Abramovich and A. W. Wickstead. In this note we construct a new type AW -space and call it CDr 0 ...

A topological space X is Baire if the intersection of any sequence open dense subsets in X. Let $$C_p(X,[0,1])$$ denote all continuous [0, 1]-valued functions on a Tychonoff with topology pointwise convergence. In this paper, we have obtained characterization for function to be separable closed which are $$C^*$$ -embedded. particular, holds normal spaces and, hence, metrizable spaces. Moreover,...

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...