In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...

The continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples. Running head: Generalized Continuity Equation E-mail: bbagch...

s In respect of the de finition of intuitionistic fuzzy n-norm [9] , the definition of generalised intuitionistic fuzzy ψ norm ( in short GIFψN ) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy ψ normed linear space and finite dimensional generalized intuitionistic fuzzy ψ normed linear space have been developed. Lastly, we have introduced the...

In this article, we establish sufficient conditions for the solution sets of parametric generalized quasi-variational relation problems with the stability properties such as the upper semicontinuity, lower semi-continuity, the Hausdorff lower semicontinuity, continuity, Hausdorff continuity, and closedness. Our results improve recent existing ones in the literature. Mathematics Subject Classifi...

In this paper we deal with a concrete example of a generalized topological space and we shall examine some topological properties such as, the usual continuity, the net-continuity and the net-closure property for it. We will show that a generalized topological space has net-continuous property or net-closure property if and only if it is a topological space. Finally we give examples of continuo...

The intent of this paper is to extend the notions of occasionally weakly compatible mappings, subcompatibility and subsequential continuity in framework of generalized metric spaces and prove some common fixed point theorems. We give some examples which demonstrate the validity of the hypotheses and degree of generality of our results. Our results are independent of the continuity requirement o...

in this paper, we have de ned and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are de ned by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

Levine , N., Semi-open sets and semi-continuity in topological spaces, Amer.Math.Monthly,70(1963),36-41. Levine , N., Generalized closed sets in topology, Rend. Circ. Mat. Palermo, 19(1970),89-96. Maki., Devi, R., and Balachandran, K., Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. Part III, 42(1993), 13-21. Hatir, E., Noiri, T., and Yuksel, S., A decomposition of continuity, Ac...

It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge. This continuity or stability is used to obtain information about invariant probability measures. It is shown that there exists an invariant p...